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Flow by $\sigma _k$ curvature to the Orlicz Christoffel-Minkowski problem
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by Caihong Yi;

Proc. Amer. Math. Soc. 152 (2024), 357-369

DOI: https://doi.org/10.1090/proc/16621

Published electronically: September 20, 2023

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Abstract:

In this paper, we consider the anisotropic curvature flow of smooth, origin-symmetric, uniformly convex hypersurfaces in $\mathbb {R}^{n+1}$. The flow exists for all time and converges smoothly to a solution of the even Orlicz Christoffel-Minkowski problem. Our proof also gives an approach to the solution of the $L_p$ Christoffel-Minkowski problem.

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