On the uniqueness of even $L^p$ Minkowski problem

Fuente: arXiv
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Main Authors: He, Weiyong, Liu, Junbang
Format: Preprint
Published: 2025
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author He, Weiyong
Liu, Junbang
author_facet He, Weiyong
Liu, Junbang
contents We prove that there is a unique $p_0\in [0,1)$, which can be characterized by the eigenvalue of Hilbert operator related to a convex body, that the even $L^p$ Minkowski problem has a unique solution for $p\geq p_0$, and the uniqueness fails for infinitely many convex bodies if $p<p_0$. The previous results by many experts in the field assert that the uniqueness holds for $p>p_0$.
format Preprint
id arxiv_https___arxiv_org_abs_2510_21530
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle On the uniqueness of even $L^p$ Minkowski problem
He, Weiyong
Liu, Junbang
Metric Geometry
Analysis of PDEs
Differential Geometry
We prove that there is a unique $p_0\in [0,1)$, which can be characterized by the eigenvalue of Hilbert operator related to a convex body, that the even $L^p$ Minkowski problem has a unique solution for $p\geq p_0$, and the uniqueness fails for infinitely many convex bodies if $p<p_0$. The previous results by many experts in the field assert that the uniqueness holds for $p>p_0$.
title On the uniqueness of even $L^p$ Minkowski problem
topic Metric Geometry
Analysis of PDEs
Differential Geometry
url https://arxiv.org/abs/2510.21530