{"paper":{"title":"Observations on gaussian upper bounds for Neumann heat kernels","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"El Maati Ouhabaz, Laurent Kayser (IECL), Mourad Choulli (IECL)","submitted_at":"2015-02-24T10:02:04Z","abstract_excerpt":"Given a domain $\\Omega$ of a complete Riemannian manifold $\\mathcal{M}$ and define $\\mathcal{A}$ to be the Laplacian with Neumann boundary condition on $\\Omega$. We prove that, under appropriate conditions, the corresponding heat kernel satisfies the  Gaussian upper bound\n$$\nh(t,x,y)\\leq \\frac{C}{\\left[V\\_\\Omega(x,\\sqrt{t})V\\_\\Omega (y,\\sqrt{t})\\right]^{1/2}}\\left( 1+\\frac{d^2(x,y)}{4t}\\right)^{\\delta}e^{-\\frac{d^2(x,y)}{4t}},\\;\\; t\\textgreater{}0,\\; x,y\\in \\Omega .\n$$\nHere $d$ is the geodesic distance on $\\mathcal{M}$, $V\\_\\Omega (x,r)$ is the Riemannian volume of $B(x,r)\\cap \\Omega$, where $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.06740","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}