https://neckpinch.com/authors/weidong-wang/New arXiv papers by Weidong Wang, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2305.14830/arxiv:2305.14830Wed, 24 May 2023 00:00:00 GMTBin Chen, Weidong Wang, Xia Zhao, Peibiao Zhao — In [Calc. Var., 57:5 (2018)], Hong-Ye-Zhang proposed the p-capacitary Orlicz-Minkowski problem and proved the existence of convex solutions to this problem by variational method for p∈(1,n). However, the smoothness and uniqueness of solutions are still open. Notice that the p-capacitary Orlicz-Minkowski problem can be converted equivalently to a Monge-Ampère type equation in smooth case: \beginalign fφ(h_K)|\nablaΨ|^p=τG \endalign for p∈(1,n) and some constant τ>0, where f is a positive function defined on the unit sphere 𝓢ⁿ⁻¹, φ is a continuous positive function defined in (0,+∞), and G is the Gauss curvature. In this paper, we confirm the existence of smooth solutions to p-capacitary Orlicz-Minkowski problem with p∈(1,n) for the first time by a class of inverse Gauss curvature flows, which converges smoothly to the solution of Equation (). Furthermore, we prove the uniqueness result for Equation () in a special case.Other curvature flowsGauss curvature flowKähler geometryStability & uniquenessLong-time existence & convergence