Metric Geometry

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href="/list/math.MG/recent?skip=11&show=50"> Mon, 17 Mar 2025 </a> </li></ul> <p>See today's <a id="new-math.MG" aria-labelledby="new-math.MG" href="/list/math.MG/new">new</a> changes</p> <div class='paging'>Total of 13 entries </div> <div class='morefewer'>Showing up to 50 entries per page: <a href=/list/math.MG/recent?skip=0&show=25 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> <dl id='articles'> <h3>Fri, 21 Mar 2025 (showing 2 of 2 entries )</h3> <dt> <a name='item1'>[1]</a> <a href ="/abs/2503.15716" title="Abstract" id="2503.15716"> arXiv:2503.15716 </a> [<a href="/pdf/2503.15716" title="Download PDF" id="pdf-2503.15716" aria-labelledby="pdf-2503.15716">pdf</a>, <a href="https://arxiv.org/html/2503.15716v1" title="View HTML" id="html-2503.15716" aria-labelledby="html-2503.15716" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.15716" title="Other formats" id="oth-2503.15716" aria-labelledby="oth-2503.15716">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Closed BV-extension and $W^{1,1}$-extension sets </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Caputo,+E">Emanuele Caputo</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Koivu,+J">Jesse Koivu</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Lu%C4%8Di%C4%87,+D">Danka Lu膷i膰</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rajala,+T">Tapio Rajala</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 42 pages, 2 figures </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Metric Geometry (math.MG)</span>; Analysis of PDEs (math.AP); Functional Analysis (math.FA) </div> </div> </dd> <dt> <a name='item2'>[2]</a> <a href ="/abs/2503.15820" title="Abstract" id="2503.15820"> arXiv:2503.15820 </a> (cross-list from math.GR) [<a href="/pdf/2503.15820" title="Download PDF" id="pdf-2503.15820" aria-labelledby="pdf-2503.15820">pdf</a>, <a href="/format/2503.15820" title="Other formats" id="oth-2503.15820" aria-labelledby="oth-2503.15820">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The Deligne Complex for the $B_3$ Artin Group </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Goldman,+K">Katherine Goldman</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Herron,+A">Amy Herron</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 35 pages, 19 figures. Comments welcome </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Group Theory (math.GR)</span>; Metric Geometry (math.MG) </div> </div> </dd> </dl> <dl id='articles'> <h3>Thu, 20 Mar 2025 (showing 2 of 2 entries )</h3> <dt> <a name='item3'>[3]</a> <a href ="/abs/2503.15159" title="Abstract" id="2503.15159"> arXiv:2503.15159 </a> [<a href="/pdf/2503.15159" title="Download PDF" id="pdf-2503.15159" aria-labelledby="pdf-2503.15159">pdf</a>, <a href="https://arxiv.org/html/2503.15159v1" title="View HTML" id="html-2503.15159" aria-labelledby="html-2503.15159" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.15159" title="Other formats" id="oth-2503.15159" aria-labelledby="oth-2503.15159">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Characterising 1-rectifiable metric spaces via connected tangent spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bate,+D">David Bate</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Valentine,+P">Phoebe Valentine</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Metric Geometry (math.MG)</span> </div> </div> </dd> <dt> <a name='item4'>[4]</a> <a href ="/abs/2503.14548" title="Abstract" id="2503.14548"> arXiv:2503.14548 </a> [<a href="/pdf/2503.14548" title="Download PDF" id="pdf-2503.14548" aria-labelledby="pdf-2503.14548">pdf</a>, <a href="https://arxiv.org/html/2503.14548v1" title="View HTML" id="html-2503.14548" aria-labelledby="html-2503.14548" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.14548" title="Other formats" id="oth-2503.14548" aria-labelledby="oth-2503.14548">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A very short proof of the Figiel-Lindenstrauss-Milman theorem </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Milo,+T">Tomer Milo</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 2 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Metric Geometry (math.MG)</span> </div> </div> </dd> </dl> <dl id='articles'> <h3>Wed, 19 Mar 2025 (showing 2 of 2 entries )</h3> <dt> <a name='item5'>[5]</a> <a href ="/abs/2503.14132" title="Abstract" id="2503.14132"> arXiv:2503.14132 </a> [<a href="/pdf/2503.14132" title="Download PDF" id="pdf-2503.14132" aria-labelledby="pdf-2503.14132">pdf</a>, <a href="https://arxiv.org/html/2503.14132v1" title="View HTML" id="html-2503.14132" aria-labelledby="html-2503.14132" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.14132" title="Other formats" id="oth-2503.14132" aria-labelledby="oth-2503.14132">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> A note on Laplacian bounds, deformation properties and isoperimetric sets in metric measure spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Pasqualetto,+E">Enrico Pasqualetto</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Rajala,+T">Tapio Rajala</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 20 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Metric Geometry (math.MG)</span>; Analysis of PDEs (math.AP); Functional Analysis (math.FA) </div> </div> </dd> <dt> <a name='item6'>[6]</a> <a href ="/abs/2503.13829" title="Abstract" id="2503.13829"> arXiv:2503.13829 </a> (cross-list from math.GT) [<a href="/pdf/2503.13829" title="Download PDF" id="pdf-2503.13829" aria-labelledby="pdf-2503.13829">pdf</a>, <a href="https://arxiv.org/html/2503.13829v1" title="View HTML" id="html-2503.13829" aria-labelledby="html-2503.13829" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.13829" title="Other formats" id="oth-2503.13829" aria-labelledby="oth-2503.13829">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> From disc patterns in the plane to character varieties of knot groups </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Elzenaar,+A">Alex Elzenaar</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 29 pages, 17 figures. Comments welcomed </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Geometric Topology (math.GT)</span>; Group Theory (math.GR); Metric Geometry (math.MG) </div> </div> </dd> </dl> <dl id='articles'> <h3>Tue, 18 Mar 2025 (showing 5 of 5 entries )</h3> <dt> <a name='item7'>[7]</a> <a href ="/abs/2503.13258" title="Abstract" id="2503.13258"> arXiv:2503.13258 </a> [<a href="/pdf/2503.13258" title="Download PDF" id="pdf-2503.13258" aria-labelledby="pdf-2503.13258">pdf</a>, <a href="/format/2503.13258" title="Other formats" id="oth-2503.13258" aria-labelledby="oth-2503.13258">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Construction of self-similar energy forms and singularity of Sobolev spaces on Laakso-type fractal spaces </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Anttila,+R">Riku Anttila</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Eriksson-Bique,+S">Sylvester Eriksson-Bique</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Shimizu,+R">Ryosuke Shimizu</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 80 Pages, comments are welcome! </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Metric Geometry (math.MG)</span>; Analysis of PDEs (math.AP); Functional Analysis (math.FA) </div> </div> </dd> <dt> <a name='item8'>[8]</a> <a href ="/abs/2503.12939" title="Abstract" id="2503.12939"> arXiv:2503.12939 </a> [<a href="/pdf/2503.12939" title="Download PDF" id="pdf-2503.12939" aria-labelledby="pdf-2503.12939">pdf</a>, <a href="/format/2503.12939" title="Other formats" id="oth-2503.12939" aria-labelledby="oth-2503.12939">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> The infimal convolution structure of the Hellinger-Kantorovich distance </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=De+Ponti,+N">Nicol貌 De Ponti</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Sodini,+G+E">Giacomo Enrico Sodini</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Tamanini,+L">Luca Tamanini</a></div> <div class='list-comments mathjax'><span class='descriptor'>Comments:</span> 53 pages </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Metric Geometry (math.MG)</span>; Functional Analysis (math.FA); Optimization and Control (math.OC); Probability (math.PR) </div> </div> </dd> <dt> <a name='item9'>[9]</a> <a href ="/abs/2503.13001" title="Abstract" id="2503.13001"> arXiv:2503.13001 </a> (cross-list from cs.LG) [<a href="/pdf/2503.13001" title="Download PDF" id="pdf-2503.13001" aria-labelledby="pdf-2503.13001">pdf</a>, <a href="https://arxiv.org/html/2503.13001v1" title="View HTML" id="html-2503.13001" aria-labelledby="html-2503.13001" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.13001" title="Other formats" id="oth-2503.13001" aria-labelledby="oth-2503.13001">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Linear-Size Neural Network Representation of Piecewise Affine Functions in $\mathbb{R}^2$ </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Zanotti,+L">Leo Zanotti</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Machine Learning (cs.LG)</span>; Neural and Evolutionary Computing (cs.NE); Metric Geometry (math.MG); Machine Learning (stat.ML) </div> </div> </dd> <dt> <a name='item10'>[10]</a> <a href ="/abs/2503.11987" title="Abstract" id="2503.11987"> arXiv:2503.11987 </a> (cross-list from math.NT) [<a href="/pdf/2503.11987" title="Download PDF" id="pdf-2503.11987" aria-labelledby="pdf-2503.11987">pdf</a>, <a href="https://arxiv.org/html/2503.11987v1" title="View HTML" id="html-2503.11987" aria-labelledby="html-2503.11987" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.11987" title="Other formats" id="oth-2503.11987" aria-labelledby="oth-2503.11987">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Geometric Properties of Periodic Lattices in Function Fields </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Aranov,+N+S">Noy Soffer Aranov</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Number Theory (math.NT)</span>; Metric Geometry (math.MG) </div> </div> </dd> <dt> <a name='item11'>[11]</a> <a href ="/abs/2503.11869" title="Abstract" id="2503.11869"> arXiv:2503.11869 </a> (cross-list from math.PR) [<a href="/pdf/2503.11869" title="Download PDF" id="pdf-2503.11869" aria-labelledby="pdf-2503.11869">pdf</a>, <a href="https://arxiv.org/html/2503.11869v1" title="View HTML" id="html-2503.11869" aria-labelledby="html-2503.11869" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.11869" title="Other formats" id="oth-2503.11869" aria-labelledby="oth-2503.11869">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> On the optimal $L_p$-$L_4$ Khintchine inequality </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Bara%C5%84ski,+A">Adam Bara艅ski</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Murawski,+D">Daniel Murawski</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Nayar,+P">Piotr Nayar</a>, <a href="https://arxiv.org/search/math?searchtype=author&query=Oleszkiewicz,+K">Krzysztof Oleszkiewicz</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Probability (math.PR)</span>; Functional Analysis (math.FA); Metric Geometry (math.MG) </div> </div> </dd> </dl> <dl id='articles'> <h3>Mon, 17 Mar 2025 (showing 2 of 2 entries )</h3> <dt> <a name='item12'>[12]</a> <a href ="/abs/2503.11137" title="Abstract" id="2503.11137"> arXiv:2503.11137 </a> (cross-list from math.AG) [<a href="/pdf/2503.11137" title="Download PDF" id="pdf-2503.11137" aria-labelledby="pdf-2503.11137">pdf</a>, <a href="https://arxiv.org/html/2503.11137v1" title="View HTML" id="html-2503.11137" aria-labelledby="html-2503.11137" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2503.11137" title="Other formats" id="oth-2503.11137" aria-labelledby="oth-2503.11137">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Planar tropical caustics: trivalency and convexity </div> <div class='list-authors'><a href="https://arxiv.org/search/math?searchtype=author&query=Shkolnikov,+M">Mikhail Shkolnikov</a></div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Algebraic Geometry (math.AG)</span>; Combinatorics (math.CO); Metric Geometry (math.MG); Number Theory (math.NT); Symplectic Geometry (math.SG) </div> </div> </dd> <dt> <a name='item13'>[13]</a> <a href ="/abs/2407.08364" title="Abstract" id="2407.08364"> arXiv:2407.08364 </a> (cross-list from cs.CV) [<a href="/pdf/2407.08364" title="Download PDF" id="pdf-2407.08364" aria-labelledby="pdf-2407.08364">pdf</a>, <a href="https://arxiv.org/html/2407.08364v3" title="View HTML" id="html-2407.08364" aria-labelledby="html-2407.08364" rel="noopener noreferrer" target="_blank">html</a>, <a href="/format/2407.08364" title="Other formats" id="oth-2407.08364" aria-labelledby="oth-2407.08364">other</a>] </dt> <dd> <div class='meta'> <div class='list-title mathjax'><span class='descriptor'>Title:</span> Scalar Function Topology Divergence: Comparing Topology of 3D Objects </div> <div class='list-authors'><a href="https://arxiv.org/search/cs?searchtype=author&query=Trofimov,+I">Ilya Trofimov</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Voronkova,+D">Daria Voronkova</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Tulchinskii,+E">Eduard Tulchinskii</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Burnaev,+E">Evgeny Burnaev</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Barannikov,+S">Serguei Barannikov</a></div> <div class='list-journal-ref'><span class='descriptor'>Journal-ref:</span> ECCV 2024 </div> <div class='list-subjects'><span class='descriptor'>Subjects:</span> <span class="primary-subject">Computer Vision and Pattern Recognition (cs.CV)</span>; Machine Learning (cs.LG); Algebraic Topology (math.AT); Metric Geometry (math.MG) </div> </div> </dd> </dl> <div class='paging'>Total of 13 entries </div> <div class='morefewer'>Showing up to 50 entries per page: <a href=/list/math.MG/recent?skip=0&show=25 rel="nofollow"> fewer</a> | <span style="color: #454545">more</span> | <span style="color: #454545">all</span> </div> </div> </div> </div> </main> <footer style="clear: both;"> <div class="columns is-desktop" role="navigation" aria-label="Secondary" style="margin: -0.75em -0.75em 0.75em -0.75em">  <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul style="list-style: none; line-height: 2;"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column" style="padding: 0;"> <div class="columns"> <div class="column"> <ul style="list-style: none; 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Metric Geometry