As on arXiv
Abstract
The Minkowski problem for torsional rigidity (-torsional rigidity) was firstly studied by Colesanti and Fimiani using variational method. Moreover, Hu also studied this problem by the method of curvature flows and obtained the existence of smooth even solutions. In addition, the smooth non-even solutions to the Orlicz Minkowski problem -torsional rigidity were given by Zhao et al. through a Gauss curvature flow. The dual curvature measure and the dual Minkowski problem were first posed and considered by Huang, Lutwak, Yang and Zhang in. The dual Minkowski problem is a very important problem, which has greatly contributed to the development of the dual Brunn-Minkowski theory and extended the other types dual Minkowski problem. To the best of our knowledge, the dual Minkowski problem () torsional rigidity is still open because the dual () torsional measure is blank. Thus, it is a natural problem to consider the dual Minkowski problem for () torsional rigidity. In this paper, we introduce the -th dual -torsional measure and propose the -th dual Minkowski problem for -torsional rigidity with . Then we confirm the existence of smooth even solutions for () to the -th dual Minkowski problem for -torsional rigidity by method of a Gauss curvature flow. Specially, we also obtain the smooth non-even solutions with to this problem.
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Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
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The -th dual Minkowski problem for the -torsional rigidity corresponding to a -Hessian equation
Topics Gauss curvature flow, Geometric inequalities, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “torsional rigidity”, “dual Minkowski”, “torsional measure”
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Flow by Gauss Curvature to the Orlicz Minkowski Problem for q-torsional rigidity
Topics Gauss curvature flow, Other curvature flows, Stability & uniqueness · Same authors Xia Zhao, Peibiao Zhao · Shared terms “torsional rigidity”, “Orlicz Minkowski”, “Colesanti”
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The Minkowski problem for the -torsional rigidity
Topics Gauss curvature flow, Geometric inequalities, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “torsional rigidity”, “torsional measure”, “Minkowski”
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Flow by Gauss Curvature to the orlicz Chord Minkowski Problem
Topics Gauss curvature flow, Geometric inequalities, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “Minkowski”, “Orlicz”, “Zhao”
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Gauss curvature flow to the -Gaussian chord Minkowski problem
Topics Gauss curvature flow, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “Minkowski”, “still open”, “Huang”
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An inverse Gauss curvature flow and its application to p-capacitary Orlicz-Minkowski problem
Topics Gauss curvature flow, Other curvature flows, Stability & uniqueness · Same authors Xia Zhao, Peibiao Zhao · Shared terms “Orlicz Minkowski”, “still open”, “Zhang”
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An expanding curvature flow and the (p,q)-Christoffel-Minkowski problems
Topics Gauss curvature flow, Other curvature flows, Stability & uniqueness · Same author Peibiao Zhao · Shared terms “dual Minkowski”, “curvature measure”
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The Gauss dual Minkowski problem
Topics Gauss curvature flow, Other curvature flows, Stability & uniqueness · Shared terms “dual Minkowski”, “dual curvature”, “curvature measure”
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