Existence of non-symmetric solutions to the Gaussian Minkowski problem

DOI10.1007/s12220-022-01139-zzbMath1506.35110arXiv2207.06932OpenAlexW4313887838MaRDI QIDQ2679625

Yibin Feng, Weiru Liu, Lei Xu

Publication date: 23 January 2023

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.06932

zbMATH Keywords

existenceMonge-Ampère equationGaussian Minkowski problem

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Monge-Ampère equations (35J96)

Related Items

On the \(L_p\) Gaussian Minkowski problem, \(L_p\) Blaschke-Santaló and Petty projection inequalities in Gaussian space

Cites Work

• Unnamed Item
• Deforming a hypersurface by Gauss curvature and support function
• Dual Orlicz-Brunn-Minkowski theory
• On the Orlicz Minkowski problem for polytopes
• Interior \(W^{2,p}\) estimates for solutions of the Monge-Ampère equation
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• The even Orlicz Minkowski problem
• An expansion of convex hypersurfaces
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• Motion of hypersurfaces by Gauss curvature
• A logarithmic Gauss curvature flow and the Minkowski problem.
• A unified flow approach to smooth, even \(L_p\)-Minkowski problems
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. I
• Deforming a hypersurface by principal radii of curvature and support function
• The \(p\)-capacitary Orlicz-Hadamard variational formula and Orlicz-Minkowski problems
• Existence of solutions to the Orlicz-Minkowski problem
• The \(L_{p}\) dual Minkowski problem for \(p\) 1 and \(q\) 0
• \(L^p\) Christoffel-Minkowski problem: the case \(1< p<k+1\)
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• A class of anisotropic expanding curvature flows
• The Minkowski problem in Gaussian probability space
• The \(L_p\) dual Minkowski problem and related parabolic flows
• The \(L_p\)-Gaussian Minkowski problem
• Existence of smooth even solutions to the dual Orlicz-Minkowski problem
• A flow approach to the Musielak-Orlicz-Gauss image problem
• Smooth solutions to the Gauss image problem
• Orlicz-Minkowski flows
• General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski problem. II
• Flow by Gauss curvature to the Aleksandrov and dual Minkowski problems
• Smoothness in the \(L_p\) Minkowski problem for \(p<1\)
• Asymptotic convergence for a class of fully nonlinear curvature flows
• The dual Orlicz-Brunn-Minkowski theory
• Smooth solutions to the \(L_p\) dual Minkowski problem
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• The Orlicz-Brunn-Minkowski theory: a general framework, additions, and inequalities
• Mixed volume preserving curvature flows
• A flow method for the dual Orlicz–Minkowski problem
• Degree Theory for Second Order Nonlinear Elliptic Operators and its Applications
• A CERTAIN PROPERTY OF SOLUTIONS OF PARABOLIC EQUATIONS WITH MEASURABLE COEFFICIENTS
• Shapes of worn stones
• On the discrete Orlicz Minkowski problem
• Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature
• Convex Bodies The Brunn-MinkowskiTheory
• An anisotropic shrinking flow and \(L_p\) Minkowski problem