The Minkowski problem in Gaussian probability space

DOI10.1016/j.aim.2021.107769zbMath1466.52010arXiv2010.00395OpenAlexW3157231314MaRDI QIDQ2032944

Yiming Zhao, Dongmeng Xi, Yong Huang

Publication date: 14 June 2021

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2010.00395

zbMATH Keywords

degree theoryMonge-Ampère equationsMinkowski problemsGaussian Minkowski problem

Mathematics Subject Classification ID

Inequalities and extremum problems involving convexity in convex geometry (52A40) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Monge-Ampère equations (35J96)

Related Items (15)

The log-Minkowski inequality of curvature entropy ⋮ On the \(L_p\) Gaussian Minkowski problem ⋮ Weighted Minkowski’s existence theorem and projection bodies ⋮ Existence of non-symmetric solutions to the Gaussian Minkowski problem ⋮ \textit{A priori} bounds, existence, and uniqueness of smooth solutions to an anisotropic \(L_p\) Minkowski problem for log-concave measure ⋮ Continuity of the solution to the \(L_p\) Minkowski problem in Gaussian probability space ⋮ The \(L_p\) chord Minkowski problem ⋮ On the planar Gaussian-Minkowski problem ⋮ \(L_p\) Blaschke-Santaló and Petty projection inequalities in Gaussian space ⋮ Prescribed \(L_p\) curvature problem ⋮ On the existence of solutions to the Orlicz-Minkowski problem for torsional rigidity ⋮ Unnamed Item ⋮ The \(L_p\)-Gaussian Minkowski problem ⋮ Uniqueness of solutions to the logarithmic Minkowski problem in \(\mathbb{R}^3\) ⋮ The \(L_p\) John ellipsoids for general measures

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