Document Zbl 1481.53047

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Math. Phys.</a> <a href="/?q=in%3A467196" title="Articles in this Issue">386, No. 1, 253-268 (2021)</a>. </div> <div class="abstract">An initial data set $(M^n, g, K)$ is a Riemannian manifold $(M, g)$ equipped with the symmetric $(0, 2)$-tensor $K$. Initial data sets have had an important role in solving the Einstein constraint equations, in geometric measure theory and in mathematical physics. Several authors study the initial data sets [<span class="zbmathjax-textit">D. A. Lee</span>, Geometric relativity. Providence, RI: American Mathematical Society (AMS) (2019; <a href="/07124831">Zbl 07124831</a>); the third author, Trans. Am. Math. Soc., (8) 372, 5851–5868 (2019; <a href="/1439.53043">Zbl 1439.53043</a>); the second author, Gen. Relativity Gravit. (3) 50, Art. 32, 7 p. (2018; <a href="/1392.83005">Zbl 1392.83005</a>); <span class="zbmathjax-textit">E. Bryden</span> et al., J. Geom. Anal. 31, No. 4, 4191–4239 (2021; <a href="/1466.83022">Zbl 1466.83022</a>); <span class="zbmathjax-textit">E. Bryden</span>, Pac. J. Math., 305, 89–152 (2020; <a href="/1435.53033">Zbl 1435.53033</a>); the first author et al., J. Eur. Math. Soc. (JEMS) 18, No. 1, 83–121 (2016; <a href="/1341.53067">Zbl 1341.53067</a>)].<br class="zbmathjax-paragraph">The principal objective in this paper is to prove rigidity results for the spacetime positive mass theorem. The authors investigate the rigidity result for the marginally outer trapped surface in $n$-dimensional, $3\leq n \leq 7$, compact-with-boundary initial data sets (Theorem 1.2, Theorem 1.3 and Corollary 1.4).<div class="reviewer"> Reviewer: <a href="/authors/?q=rv%3A18008">Lakehal Belarbi (Mostaganem)</a></div> <div class="clearfix"></div></div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7376274">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7376274">Cited in <strong>11</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A53C20" title="MSC2020">53C20</a> </td> <td class="space"> Global Riemannian geometry, including pinching </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A53B30" title="MSC2020">53B30</a> </td> <td class="space"> Local differential geometry of Lorentz metrics, indefinite metrics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Apositive+mass+theorem">positive mass theorem</a>; <a href="/?q=ut%3Alocal+energy+density">local energy density</a>; <a href="/?q=ut%3Alocal+current+density">local current density</a>; <a href="/?q=ut%3AADM+energy-momentum+vector">ADM energy-momentum vector</a>; <a href="/?q=ut%3Adominant+energy+condition">dominant energy condition</a>; <a href="/?q=ut%3AMinkowski+space">Minkowski space</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1439.53043">Zbl 1439.53043</a>; <a href="/1392.83005">Zbl 1392.83005</a>; <a href="/1466.83022">Zbl 1466.83022</a>; <a href="/1435.53033">Zbl 1435.53033</a>; <a href="/1341.53067">Zbl 1341.53067</a>; <a href="/07124831">Zbl 07124831</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1481.53047" data-ciurl="/ci/07376274" data-biburl="/bibtex/07376274.bib" data-amsurl="/amsrefs/07376274.bib" data-xmlurl="/xml/07376274.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07376274.pdf" title="Zbl 1481.53047 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s00220-021-04033-x" aria-label="DOI for “Initial data rigidity results”" title="10.1007/s00220-021-04033-x">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2009.09527"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Alaee, A., Lesourd, M., Yau, S.-T.: Stable Surfaces and Free Boundary Marginally Outer Trapped Surfaces (preprint). arXiv:2009.07933 (2020)</td> </tr><tr> <td>[2]</td> <td class="space">Andersson, L.; Cai, M-L; Galloway, GJ, Rigidity and positivity of mass for asymptotically hyperbolic manifolds, Ann. 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This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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