Ancient Solutions to the Biharmonic Heat Equation
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911472672571392 |
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| author | McWeeney, Alexander D. |
| author_facet | McWeeney, Alexander D. |
| contents | We show that the space of polynomially bounded ancient solutions to the biharmonic heat equation on a complete manifold with polynomial volume growth is bounded by the dimensions of spaces of polynomially bounded biharmonic functions. This generalizes the work of Colding and Minicozzi in [6] for ancient caloric functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_13952 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ancient Solutions to the Biharmonic Heat Equation McWeeney, Alexander D. Differential Geometry Analysis of PDEs We show that the space of polynomially bounded ancient solutions to the biharmonic heat equation on a complete manifold with polynomial volume growth is bounded by the dimensions of spaces of polynomially bounded biharmonic functions. This generalizes the work of Colding and Minicozzi in [6] for ancient caloric functions. |
| title | Ancient Solutions to the Biharmonic Heat Equation |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2512.13952 |