https://neckpinch.com/authors/bin-chen/New arXiv papers by Bin Chen, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2305.14830arxiv: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 https://arxiv.org/abs/2203.05105arxiv:2203.05105Thu, 10 Mar 2022 00:00:00 GMTBin Chen, Jingshi Cui, Peibiao Zhao — The present paper introduces a new class of geometric measures, the k-th (p,q)-mixed curvature measures, and a natural correspondence-(p,q)-Christoffel-Minkowski problem is proposed. The (p,q)-Christoffel-Minkowski problem posed here can be regarded as a natural generalization of the L_p Christoffel-Minkowski problem and Lp dual Minkowski problem. We investigate and arrive at the existence of smooth solution to the (p,q)-Christoffel-Minkowski problem by a type of expanding curvature flow. Furthermore, the uniqueness result of solutions to the (p,q)-Christoffel-Minkowski problem shall be discussed.Other curvature flowsGauss curvature flowLimit spaces & RCDStability & uniqueness https://arxiv.org/abs/2111.13281arxiv:2111.13281Fri, 26 Nov 2021 00:00:00 GMTBin Chen, Peibiao Zhao — In this paper we first obtain the existence of smooth solutions to Orlicz-Aleksandrov problem via a Gauss-like curvature flow.Other curvature flowsGauss curvature flow