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This is a Quantitative Study study.

October 5, 2025Open Access

The Lₚ chord Minkowski problem for super-critical exponent

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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.

Implication

This research addresses the $L_p$ chord measure on convex bodies, suggesting new conditions for super-critical exponents.

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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Cite This Study

Chen et al. (2025) studied this question.

synapsesocial.com/papers/68e2537cd6d66a53c24743e7 https://doi.org/10.48550/arxiv.2510.01084

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Implication

This research addresses the $L_p$ chord measure on convex bodies, suggesting new conditions for super-critical exponents.

The Lₚ chord Minkowski problem for super-critical exponent

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Implication

Abstract

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Cite This Study

The Lₚ chord Minkowski problem for super-critical exponent

Key Points

Implication

Abstract

Discussion

Cite This Study

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