A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866910033002889216 |
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| author | Colesanti, A. Focardi, M. Guan, P. Salani, P. |
| author_facet | Colesanti, A. Focardi, M. Guan, P. Salani, P. |
| contents | We study the mixed Christoffel problem for $C^{2,+}$ convex bodies providing sufficient conditions for its solution. Key to our approach is a constant rank theorem, following the approach developed in \cite{Guan-Ma-2003} to address the Christoffel problem, in order to ensure that the solution to a related second order linear PDE on the sphere is indeed geometric, that is, it is the support functions of a $C^{2,+}$ convex body. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem Colesanti, A. Focardi, M. Guan, P. Salani, P. Analysis of PDEs Metric Geometry 52A20, 35J15 We study the mixed Christoffel problem for $C^{2,+}$ convex bodies providing sufficient conditions for its solution. Key to our approach is a constant rank theorem, following the approach developed in \cite{Guan-Ma-2003} to address the Christoffel problem, in order to ensure that the solution to a related second order linear PDE on the sphere is indeed geometric, that is, it is the support functions of a $C^{2,+}$ convex body. |
| title | A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem |
| topic | Analysis of PDEs Metric Geometry 52A20, 35J15 |
| url | https://arxiv.org/abs/2512.08670 |