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October 5, 2025Open Access

The Lₚ chord Minkowski problem for super-critical exponent

Key Points

The $L_p$ chord Minkowski problem provides essential conditions for specific convex bodies, allowing broader applications.
The study resolves challenges posed by super-critical exponents using advanced curvature flow methods and topological concepts.
Nonlocal Gauss curvature flow offers a new perspective in mathematical analysis for understanding convex geometry.
The findings simplify previous topological arguments, enhancing their applicability in the broader mathematical context.

Abstract

The Lₚ chord Minkowski problem was recently introduced by Lutwak, Xi, Yang and Zhang, which seeks to determine the necessary and sufficient conditions for a given finite Borel measure such that it is the Lₚ chord measure of a convex body. In this paper, we solve the Lₚ chord Minkowski problem for the super-critical exponents by combining a nonlocal Gauss curvature flow introduced in HHLW exi and a topological argument developed in GLW2022. Notably, we provide a simplified argument for the topological part.

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