Work

Curvature bound for L Minkowski problem

Year: 2024

Type: article

Abstract: We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure μ with a positive smooth density f , any solution to the L p Minkowski problem in R n + 1 with p ≤ − n + 2 is a hypersurface of class C 1 , 1 . This is a sharp result because for each p ∈ [ − n + 2 , 1 ) there exists a convex hypersurface of class C 1 , 1 n + p − 1 which is a solution to the L p Minkowski problem for a positive smooth density f . In particular, the C 1 , 1 regularity is optimal in the case p = − n + 2 which includes the logarithmic Minkowski problem in R 3 .

Source: Advances in Mathematics

DOI: 10.1016/j.aim.2024.109959

Authors: Kyeongsu Choi, Minhyun Kim, Taehun Lee

Institutions: Korea Institute for Advanced Study, Hanyang University

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,510

Funders: Hanyang University, National Research Foundation of Korea, Korea Institute for Advanced Study