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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.09711 |
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| _version_ | 1866910833941938176 |
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| author | Lin, Fanghua Qiu, Hongbing Sun, Jun Zhang, Qi S. |
| author_facet | Lin, Fanghua Qiu, Hongbing Sun, Jun Zhang, Qi S. |
| contents | Under a condition that breaks the volume doubling barrier, we obtain a time polynomial structure result on the space of ancient caloric functions with polynomial growth on manifolds.
As a byproduct, it is shown that the finiteness result for the space of harmonic functions with polynomial growth on manifolds in \cite{CM97} and \cite{Li97} are essentially sharp, except for the multi-end cases, addressing an issue raised in \cite{CM98} and removing all {\it local} topological or geometric conditions on the manifold with respect to a reference point. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_09711 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Space of ancient caloric functions on some manifolds beyond volume doubling Lin, Fanghua Qiu, Hongbing Sun, Jun Zhang, Qi S. Differential Geometry Analysis of PDEs 58J35, 53C44 Under a condition that breaks the volume doubling barrier, we obtain a time polynomial structure result on the space of ancient caloric functions with polynomial growth on manifolds. As a byproduct, it is shown that the finiteness result for the space of harmonic functions with polynomial growth on manifolds in \cite{CM97} and \cite{Li97} are essentially sharp, except for the multi-end cases, addressing an issue raised in \cite{CM98} and removing all {\it local} topological or geometric conditions on the manifold with respect to a reference point. |
| title | Space of ancient caloric functions on some manifolds beyond volume doubling |
| topic | Differential Geometry Analysis of PDEs 58J35, 53C44 |
| url | https://arxiv.org/abs/2501.09711 |