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arXiv · 2512.08670

A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem

A. Colesanti·M. Focardi·P. Guan·P. Salani
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Abstract

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.

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A. Colesanti, M. Focardi, P. Guan, P. Salani. 2025-12-09. A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem. https://arxiv.org/abs/2512.08670

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