Optimal Hamilton-type gradient estimates for the heat equation on noncompact manifolds
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909691437645824 |
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| author | Chabi, Loth Damagui Souplet, Philippe |
| author_facet | Chabi, Loth Damagui Souplet, Philippe |
| contents | We derive localized and global noncompact versions of Hamilton's gradient estimate
for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below.
Our estimates are essentially optimal and significantly improve on all previous estimates of this type.
As applications, we derive a new
and sharp, space only, local pseudo-Harnack inequality, as well as estimates of the spatial modulus of continuity of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12190 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Hamilton-type gradient estimates for the heat equation on noncompact manifolds Chabi, Loth Damagui Souplet, Philippe Analysis of PDEs Differential Geometry We derive localized and global noncompact versions of Hamilton's gradient estimate for positive solutions to the heat equation on Riemannian manifolds with Ricci curvature bounded below. Our estimates are essentially optimal and significantly improve on all previous estimates of this type. As applications, we derive a new and sharp, space only, local pseudo-Harnack inequality, as well as estimates of the spatial modulus of continuity of solutions. |
| title | Optimal Hamilton-type gradient estimates for the heat equation on noncompact manifolds |
| topic | Analysis of PDEs Differential Geometry |
| url | https://arxiv.org/abs/2507.12190 |