On monotonicity of heat kernels: a new example and counterexamples
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866913687901569024 |
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| author | Burchard, Almut Martínez, Ángel D. |
| author_facet | Burchard, Almut Martínez, Ángel D. |
| contents | We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity property. Furthermore, we show that for a generic metric on any smooth manifold the monotonicity property fails at large times. This answers a recent question of Alonso-Orán, Chamizo, Martínez, and Mas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08212 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On monotonicity of heat kernels: a new example and counterexamples Burchard, Almut Martínez, Ángel D. Differential Geometry Analysis of PDEs Classical Analysis and ODEs We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity property. Furthermore, we show that for a generic metric on any smooth manifold the monotonicity property fails at large times. This answers a recent question of Alonso-Orán, Chamizo, Martínez, and Mas. |
| title | On monotonicity of heat kernels: a new example and counterexamples |
| topic | Differential Geometry Analysis of PDEs Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2502.08212 |