Gradient estimates for heat-type equations on manifolds evolving by the Ricci flow (Q2878921)
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scientific article; zbMATH DE number 6340613
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Gradient estimates for heat-type equations on manifolds evolving by the Ricci flow |
scientific article; zbMATH DE number 6340613 |
Statements
5 September 2014
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conjugate heat equation
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Harnack inequalities
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Laplace-Beltrami operator
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Laplacian comparison theorem
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0.96844786
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0.9670563
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0.9625721
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0.9571126
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0.9552674
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0.94023335
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0.93579245
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Gradient estimates for heat-type equations on manifolds evolving by the Ricci flow (English)
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In the recent years, starting from the seminal work by Hamilton, many papers studied the geometric heat equation coupled to the Ricci flow. In this paper, the author considers such a question proving certain localized and global gradient estimates for all positive solutions. More precisely, the author couples the Ricci flow to the geometric heat equation either forward, backward and perturbed with curvature operator and, as a by product, the author obtains various Li-Yau type differential Harnack estimates.
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