{"paper":{"title":"The spectrum of the Laplacian on closed manifolds and the heat asymptotics near conical points","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.AP","authors_text":"Nikolaos Roidos","submitted_at":"2023-12-01T13:28:35Z","abstract_excerpt":"Let $\\mathcal{M}$ be a smooth, closed and connected manifold of dimension $n\\in\\mathbb{N}$, endowed with a Riemannian metric $g$. Moreover, let $\\mathcal{B}$ be an $(n+1)$-dimensional compact manifold with boundary equal to $\\mathcal{M}$. Endow $\\mathcal{B}$ with a Riemannian metric $h$ such that, in local coordinates $(x,y)\\in [0,1)\\times \\mathcal{M}$ on the collar part of the boundary, it admits the warped product form $h=dx^{2}+x^{2}g(y)$. We consider the homogeneous heat equation on $(\\mathcal{B},h)$ and find an arbitrary long asymptotic expansion of the solutions with respect to $x$ near "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2312.00573","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2312.00573/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}