On the second Robin eigenvalue of the Laplacian [article]

Xiaolong Li, Kui Wang, Haotian Wu
<span title="2020-03-06">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We study the Robin eigenvalue problem for the Laplace-Beltrami operator on Riemannian manifolds. Our first result is a comparison theorem for the second Robin eigenvalue on geodesic balls in manifolds whose sectional curvatures are bounded from above. Our second result asserts that geodesic balls in nonpositively curved space forms maximize the second Robin eigenvalue among bounded domains of the same volume.
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2003.03087v1">arXiv:2003.03087v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kiau5fhssnf4nendlxmjzk5r5i">fatcat:kiau5fhssnf4nendlxmjzk5r5i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200322122329/https://arxiv.org/pdf/2003.03087v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2003.03087v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>