Prescribed \(L_p\) curvature problem

DOI10.1016/j.aim.2024.109566arXiv2312.02122OpenAlexW4392328975MaRDI QIDQ6204532

Mohammad N. Ivaki, Yingxiang Hu

Publication date: 28 March 2024

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

Full work available at URL: https://arxiv.org/abs/2312.02122

zbMATH Keywords

\(L_p\)-Christoffel-Minkowski problem\(L_p\)-curvature problem

Mathematics Subject Classification ID

Elliptic equations and elliptic systems (35Jxx) Global differential geometry (53Cxx) General convexity (52Axx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multiple solutions of the \(L_{p}\)-Minkowski problem
• Closed hypersurfaces with prescribed Weingarten curvature in Riemannian manifolds
• Hypersurfaces of prescribed curvature measure
• The log-Brunn-Minkowski inequality
• \(\mathrm{SL}(n)\) invariant valuations on polytopes
• The Brunn-Minkowski-Firey theory. I: Mixed volumes and the Minkowski problem
• Convex hypersurfaces of prescribed Weingarten curvatures
• Embedded hyperspheres with prescribed mean curvature
• A localization property of viscosity solutions to the Monge-Ampère equation and their strict convexity
• Closed Weingarten hypersurfaces in Riemannian manifolds
• Hypersurfaces of prescribed Weingarten curvature
• The Christoffel-Minkowski problem. I: Convexity of solutions of a Hessian equation
• A logarithmic Gauss curvature flow and the Minkowski problem.
• \(L_ p\) affine isoperimetric inequalities.
• A unified flow approach to smooth, even \(L_p\)-Minkowski problems
• The \(L_{p}\)-Minkowski problem for \(-n < p < 1\)
• Deforming a hypersurface by principal radii of curvature and support function
• Asymptotic behavior of flows by powers of the Gaussian curvature
• Uniqueness of closed self-similar solutions to \(\sigma_k^\alpha\)-curvature flow
• Starshaped compact hypersurfaces with prescribed Weingarten curvature in warped product manifolds
• \(L^p\) Christoffel-Minkowski problem: the case \(1< p<k+1\)
• Sharp affine \(L_ p\) Sobolev inequalities.
• Convex hypersurfaces of prescribed curvatures
• On the Christoffel-Minkowski problem of Firey's \(p\)-sum
• On the regularity of solutions to a generalization of the Minkowski problem
• The Brunn-Minkowski-Firey theory. II: Affine and geominimal surface areas
• On the regularity of the \(L_p\) Minkowski problem
• Parabolic approaches to curvature equations
• The Minkowski problem in Gaussian probability space
• The Christoffel problem by the fundamental solution of the Laplace equation
• The \(L_p\) Minkowski type problem for a class of mixed Hessian quotient equations
• The \(L_p\)-Brunn-Minkowski inequality for \(p<1\)
• The \(L_p\)-Minkowski problem and the Minkowski problem in centroaffine geometry
• Minkowskische Integralformeln und ihre Anwendungen in der Differentialgeometrie im Großen
• Intermediate Christoffel-Minkowski problems for figures of revolution
• The Dirichlet problem for the prescribed curvature equations
• The Christoffel-Minkowski problem. II: Weingarten curvature equations
• Constant rank theorems for curvature problems via a viscosity approach
• Degree Theory for Second Order Nonlinear Elliptic Operators and its Applications
• Some existence results for fully nonlinear elliptic equations of monge-ampère type
• Closed Convex Hypersurfaces with Curvature Restrictions
• Nonlinear second-order elliptic equations V. The dirichlet problem for weingarten hypersurfaces
• On the regularity of the solution of then-dimensional Minkowski problem
• On the $L_{p}$-Minkowski problem
• The logarithmic Minkowski problem
• Infinitely Many Solutions for Centro-affine Minkowski Problem
• Global C²‐Estimates for Convex Solutions of Curvature Equations
• Convex Bodies The Brunn-MinkowskiTheory
• The Christofel‐Minkowski problem III: Existence and convexity of admissible solutions
• The determination of convex bodies from their mean radius of curvature functions
• The Weyl and Minkowski problems in differential geometry in the large
• Christoffel-Minkowski flows
• Uniqueness of solutions to a class of isotropic curvature problems

This page was built for publication: Prescribed \(L_p\) curvature problem