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<button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2110.12413">arXiv:2110.12413</a> <span> [<a href="https://arxiv.org/pdf/2110.12413">pdf</a>, <a href="https://arxiv.org/ps/2110.12413">ps</a>, <a href="https://arxiv.org/format/2110.12413">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Spectral Theory">math.SP</span> </div> </div> <p class="title is-5 mathjax"> CR embeddability of quotients of the Rossi sphere via spectral theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bosch%2C+H">Henry Bosch</a>, <a href="/search/math?searchtype=author&query=Gonzales%2C+T">Tyler Gonzales</a>, <a href="/search/math?searchtype=author&query=Spinelli%2C+K">Kamryn Spinelli</a>, <a href="/search/math?searchtype=author&query=Udell%2C+G">Gabe Udell</a>, <a href="/search/math?searchtype=author&query=Zeytuncu%2C+Y+E">Yunus E. Zeytuncu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2110.12413v1-abstract-short" style="display: inline;"> We look at the action of finite subgroups of $\operatorname{SU}(2)$ on $S^3$, viewed as a CR manifold, both with the standard CR structure as the unit sphere in $\mathbb{C}^2$ and with a perturbed CR structure known as the Rossi sphere. We show that quotient manifolds from these actions are indeed CR manifolds, and relate the order of the subgroup of $\operatorname{SU}(2)$ to the asymptotic distri… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.12413v1-abstract-full').style.display = 'inline'; document.getElementById('2110.12413v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2110.12413v1-abstract-full" style="display: none;"> We look at the action of finite subgroups of $\operatorname{SU}(2)$ on $S^3$, viewed as a CR manifold, both with the standard CR structure as the unit sphere in $\mathbb{C}^2$ and with a perturbed CR structure known as the Rossi sphere. We show that quotient manifolds from these actions are indeed CR manifolds, and relate the order of the subgroup of $\operatorname{SU}(2)$ to the asymptotic distribution of the Kohn Laplacian's eigenvalues on the quotient. We show that the order of the subgroup determines whether the quotient of the Rossi sphere by the action of that subgroup is CR embeddable. Finally, in the unperturbed case, we prove that we can determine the size of the subgroup by using the point spectrum. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2110.12413v1-abstract-full').style.display = 'none'; document.getElementById('2110.12413v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 24 October, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2010.04568">arXiv:2010.04568</a> <span> [<a href="https://arxiv.org/pdf/2010.04568">pdf</a>, <a href="https://arxiv.org/ps/2010.04568">ps</a>, <a href="https://arxiv.org/format/2010.04568">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="Complex Variables">math.CV</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Spectral Theory">math.SP</span> </div> </div> <p class="title is-5 mathjax"> A Tauberian Approach to Weyl's Law for the Kohn Laplacian on Spheres </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/math?searchtype=author&query=Bosch%2C+H">Henry Bosch</a>, <a href="/search/math?searchtype=author&query=Gonzales%2C+T">Tyler Gonzales</a>, <a href="/search/math?searchtype=author&query=Spinelli%2C+K">Kamryn Spinelli</a>, <a href="/search/math?searchtype=author&query=Udell%2C+G">Gabe Udell</a>, <a href="/search/math?searchtype=author&query=Zeytuncu%2C+Y+E">Yunus E. Zeytuncu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2010.04568v1-abstract-short" style="display: inline;"> We compute the leading coefficient in the asymptotic expansion of the eigenvalue counting function for the Kohn Laplacian on the spheres. We express the coefficient as an infinite sum and as an integral. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2010.04568v1-abstract-full" style="display: none;"> We compute the leading coefficient in the asymptotic expansion of the eigenvalue counting function for the Kohn Laplacian on the spheres. We express the coefficient as an infinite sum and as an integral. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2010.04568v1-abstract-full').style.display = 'none'; document.getElementById('2010.04568v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 9 October, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">MSC Class:</span> 32V05; 32V20 </p> </li> </ol> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> 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