Analysis and Geometry in Metric Spaces

Inserted: 24 nov 2022
Last Updated: 24 nov 2022

Volume: 10
Year: 2022
Doi: https://doi.org/10.1515/agms-2022-0146

Abstract:

Liu and Lu $[27]$ investigated a generalized Gauss curvature flow and obtained an even solution to the dual Orlicz-Minkowski problem under some appropriate assumptions. The present paper investigates a inverse Gauss curvature flow, and achieves the long-time existence and convergence of this flow via a different $C^0$-estimate technique under weaker conditions. As an application of this inverse Gauss curvature flow, the present paper first arrives at a non-even smooth solution to the Orlicz Minkowski problem.