https://neckpinch.com/authors/ke-xue/New arXiv papers by Ke Xue, from Neckpinch Tue, 03 Nov 2026 08:37:45 GMT https://neckpinch.com/papers/2212.01822/arxiv:2212.01822Sun, 04 Dec 2022 00:00:00 GMTWeimin Sheng, Ke Xue — In this paper, we study the Lₚ-Gaussian Minkowski problem, which arises in the Lₚ-Brunn-Minkowski theory in Gaussian probability space. We use Aleksandrov's variational method with Lagrange multipliers to prove the existence of the logarithmic Gauss Minkowski problem. We construct a suitable Gauss curvature flow of closed, convex hypersurfaces in the Euclidean space ℝⁿ⁺¹, and prove its long-time existence and converges smoothly to a smooth solution of the normalized Lₚ Gaussian Minkowski problem in cases of p>0 and −n-1<p≤ 0 with even prescribed function respectively. We also provide a parabolic proof in the smooth category to the Lₚ-Gaussian Minkowski problem in cases of p≥ n+1 and 0<p<n+1 with even prescribed function, respectively.Other curvature flowsGauss curvature flowLong-time existence & convergenceGeometric inequalities