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Uniqueness of solutions to a class of non-homogeneous curvature problems
- Publication Year :
- 2023
-
Abstract
- We show that the only even, smooth, convex solutions to a class of isotropic mixed Christoffel-Minkowski type problems are origin-centred spheres, which, in particular, answers a question of Firey 74 in the even isotropic case about kinematic measures. Employing the Heintze-Karcher inequality, we prove that the only smooth, strictly convex solutions to a large class of Minkowski type problems are origin-centred spheres. Immediate corollaries are the uniqueness of solutions to the isotropic Orlicz-Minkowski problem and the isotropic $L_p$-Gaussian-Minkowski problem when $p\geq 1$.
- Subjects :
- Mathematics - Differential Geometry
Mathematics - Analysis of PDEs
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2307.06252
- Document Type :
- Working Paper