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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2014
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/1405.6373 |
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| _version_ | 1866929319508443136 |
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| author | Chen, Chuanqiang Ma, Xi-Nan Salani, Paolo |
| author_facet | Chen, Chuanqiang Ma, Xi-Nan Salani, Paolo |
| contents | In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain our ideas and for completeness, we also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1405_6373 |
| institution | arXiv |
| publishDate | 2014 |
| record_format | arxiv |
| spellingShingle | On space-time quasiconcave solutions of the heat equation Chen, Chuanqiang Ma, Xi-Nan Salani, Paolo Analysis of PDEs In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain our ideas and for completeness, we also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function. |
| title | On space-time quasiconcave solutions of the heat equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1405.6373 |