A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold

A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold

Show other versions (1)

<p>In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwi...

Full description

Bibliographic Details
Main Author: Abimbola Abolarinwa
Format: Article
Language:English
Published: Etamaths Publishing 2014-08-01
Series:International Journal of Analysis and Applications
Online Access:http://etamaths.com/index.php/ijaa/article/view/357
id doaj-06d3dc77a3e74afe80d1c238cef482c4
record_format Article
spelling doaj-06d3dc77a3e74afe80d1c238cef482c42021-08-26T13:44:36ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392014-08-016111786A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static ManifoldAbimbola Abolarinwa0UNIVERSITY OF SUSSEX, BRIGHTON, BN1 9QH, UK.<p>In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.</p>http://etamaths.com/index.php/ijaa/article/view/357
collection DOAJ
language English
format Article
sources DOAJ
author Abimbola Abolarinwa
spellingShingle Abimbola Abolarinwa
A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
International Journal of Analysis and Applications
author_facet Abimbola Abolarinwa
author_sort Abimbola Abolarinwa
title A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
title_short A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
title_full A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
title_fullStr A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
title_full_unstemmed A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
title_sort new entropy formula and gradient estimates for the linear heat equation on static manifold
publisher Etamaths Publishing
series International Journal of Analysis and Applications
issn 2291-8639
publishDate 2014-08-01
description <p>In this paper we prove a new monotonicity formula for the heat equation via a generalized family of entropy functionals. This family of entropy formulas generalizes both Perelman’s entropy for evolving metric and Ni’s entropy on static manifold. We show that this entropy satisfies a pointwise differential inequality for heat kernel. The consequences of which are various gradient and Harnack estimates for all positive solutions to the heat equation on compact manifold.</p>
url http://etamaths.com/index.php/ijaa/article/view/357
work_keys_str_mv AT abimbolaabolarinwa anewentropyformulaandgradientestimatesforthelinearheatequationonstaticmanifold
AT abimbolaabolarinwa newentropyformulaandgradientestimatesforthelinearheatequationonstaticmanifold
_version_ 1721193555409502208

Similar Items