A necessary condition for the logarithmic Minkowksi problem in higher dimension
Mijia Lai, Zixiao Wang
TL;DR
This paper presents a necessary condition for solving the logarithmic Minkowski problem in higher dimensions, extending previous two-dimensional results and refining existing subspace concentration conditions.
Contribution
It generalizes a known necessary condition to higher dimensions and improves the subspace concentration condition for the logarithmic Minkowski problem.
Findings
Established a necessary condition for higher-dimensional cases.
Extended previous two-dimensional results to higher dimensions.
Refined the subspace concentration condition.
Abstract
In this paper, we establish a necessary condition for the logarithmic Minkowski problem in higher dimensions. This result generalizes a necessary condition proposed by Liu, Lu, Sun, and Xiong in their investigation of the two-dimensional case, and also refines the so-called subspace concentration condition.
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Taxonomy
TopicsPoint processes and geometric inequalities · Nonlinear Partial Differential Equations · Fractional Differential Equations Solutions