The dual Orlicz-Minkowski problem
Baocheng Zhu, Sudan Xing, Deping Ye
TL;DR
This paper introduces the dual Orlicz curvature measure, explores its properties, and solves the dual Orlicz-Minkowski problem by establishing a variational formula that offers a geometric interpretation.
Contribution
It proposes the dual Orlicz curvature measure, derives a variational formula for the dual Orlicz-quermassintegral, and provides a solution to the dual Orlicz-Minkowski problem.
Findings
Defined the dual Orlicz curvature measure and analyzed its properties.
Established a variational formula linking the dual Orlicz-quermassintegral and the curvature measure.
Solved the dual Orlicz-Minkowski problem using the variational approach.
Abstract
In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the dual Orlicz-Minkowski problem regarding the dual Orlicz curvature measure is provided.
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Taxonomy
TopicsPoint processes and geometric inequalities · Morphological variations and asymmetry