Some gradient estimates for the heat equation on domains and for an equation by Perelman

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dc.creatorZhang, Qi S.
dc.date2006-05-18
dc.date2006-10-11
dc.date.accessioned2026-07-07T07:14:23Z
dc.date.available2026-07-07T07:14:23Z
dc.descriptionIn the first part, we derive a sharp gradient estimate for the log of Dirichlet heat kernel and Poisson heat kernel on domains, and a sharpened local Li-Yau gradient estimate that matches the global one. In the second part, without explicit curvature assumptions, we prove a global upper bound for the fundamental solution of an equation introduced by G. Perelman, i.e. the heat equation of the conformal Laplacian under backward Ricci flow. Further, under nonnegative Ricci curvature assumption, we prove a qualitatively sharp, global Gaussian upper bound.
dc.identifierhttps://arxiv.org/abs/math/0605518
dc.identifierhttp://arxiv.org/abs/math/0605518
dc.identifierInternational Math. Research Notices 2006
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/112853
dc.subjectDifferential Geometry
dc.subjectAnalysis of PDEs
dc.subject58J35, 35K20
dc.titleSome gradient estimates for the heat equation on domains and for an equation by Perelman
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