A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold
<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...
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| Format: | Article |
| Language: | English |
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Etamaths Publishing
2014-08-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/357 |
| _version_ | 1818904374114516992 |
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| author | Abimbola Abolarinwa |
| author_facet | Abimbola Abolarinwa |
| author_sort | Abimbola Abolarinwa |
| collection | DOAJ |
| 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> |
| first_indexed | 2024-12-19T21:06:25Z |
| format | Article |
| id | doaj.art-06d3dc77a3e74afe80d1c238cef482c4 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-19T21:06:25Z |
| publishDate | 2014-08-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-06d3dc77a3e74afe80d1c238cef482c42022-12-21T20:05:38ZengEtamaths 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 |
| spellingShingle | Abimbola Abolarinwa A New Entropy Formula and Gradient Estimates for the Linear Heat Equation on Static Manifold International Journal of Analysis and Applications |
| title | 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_short | 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 |
| url | http://etamaths.com/index.php/ijaa/article/view/357 |
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