Hamilton’s gradient estimates and a monotonicity formula for heat flows on metric measure spaces

In this paper, we extend the Hamilton’s gradient estimates (Hamilton 1993) and a monotonicity formula of entropy (Ni 2004) for heat flows from smooth Riemannian manifolds to (non-smooth) metric measure spaces with appropriate Riemannian curvature-dimension condition.

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Bibliographic Details
Published inNonlinear analysis Vol. 131; pp. 32 - 47
Main Authors Jiang, Renjin, Zhang, Huichun
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.01.2016
Subjects
Curvature-dimension condition
Estimates
Hamilton’s gradient estimates
Heat transfer
Heat transmission
Manifolds
Metric measure space
Nickel
Nonlinearity
35K05
Curvature-dimension condition
Metric measure space
53C23
Hamilton’s gradient estimates
Online AccessGet full text
ISSN0362-546X
1873-5215
DOI10.1016/j.na.2015.08.011

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Summary:In this paper, we extend the Hamilton’s gradient estimates (Hamilton 1993) and a monotonicity formula of entropy (Ni 2004) for heat flows from smooth Riemannian manifolds to (non-smooth) metric measure spaces with appropriate Riemannian curvature-dimension condition.
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content type line 23
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2015.08.011