Affine dual Minkowski problems

IF 1.5 1区数学 Q1 MATHEMATICS

Advances in Mathematics Pub Date : 2025-03-05 DOI:10.1016/j.aim.2025.110184

Xiaxing Cai, Gangsong Leng, Yuchi Wu, Dongmeng Xi

引用次数: 0

Abstract

While affine functionals of convex bodies and their affine isoperimetric inequalities have been extensively studied, the construction of geometric measures arising from affine geometric invariants (other than volume) has been missing.

In this work, affine ‘‘invariant’’ measures derived from the dual affine quermassintegrals are presented. Minkowski problems for the new affine-invariant measures are proposed and studied. The new variation formula derived here leads to new affine operators that map star bodies to star bodies. An affine isoperimetric inequality is obtained for new bi-dual intersection bodies.

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仿射对偶Minkowski问题

虽然凸体的仿射泛函及其仿射等周不等式已被广泛研究，但由仿射几何不变量（体积除外）引起的几何测度的构造一直缺失。在这项工作中，给出了由对偶仿射quermass积分导出的仿射“不变”测度。提出并研究了新的仿射不变测度的Minkowski问题。这里导出的新的变分公式导致了新的仿射算子，将恒星体映射到恒星体。得到了新的双对偶交体的仿射等周不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Advances in Mathematics 数学-数学

CiteScore

2.80

自引率

5.90%

发文量

497

审稿时长

7.5 months

期刊介绍： Emphasizing contributions that represent significant advances in all areas of pure mathematics, Advances in Mathematics provides research mathematicians with an effective medium for communicating important recent developments in their areas of specialization to colleagues and to scientists in related disciplines.