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Abstract
Recently, Huang and Qin introduced the Gaussian chord measure and -Gaussian chord measure by variational methods. Meanwhile, they posed Gaussian chord Minkowski problem for and used variational methods to obtain an origin-symmetric normalized measure solution for the Gaussian chord Minkowski problem. The smooth solution, up to now, to the -Gaussian chord Minkowski problem is still open. Motivated by the forgoing works by Huang and Qin in, we propose in the present paper the -Gaussian chord Minkowski problem and log-Gaussian chord Minkowski problem, and obtain the smooth even solutions to these two types of problems by the method of a Gauss curvature flow.
Comments: arXiv admin note: substantial text overlap with arXiv:2404.19266
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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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Flow by Gauss Curvature to the orlicz Chord Minkowski Problem
Topics Gauss curvature flow, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “chord Minkowski”, “chord measure”, “measure solution”
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The chord Gauss curvature flow and its chord Minkowski problem
Topics Gauss curvature flow, Other curvature flows · Shared terms “chord Minkowski”
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Flow by Gauss Curvature to the Orlicz Minkowski Problem for q-torsional rigidity
Topics Gauss curvature flow, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “Minkowski”
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The dual Minkowski problem for -torsional rigidity
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 · Same authors Xia Zhao, Peibiao Zhao · Shared terms “Minkowski”, “still open”, “smooth solutions”
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The Minkowski problem for the -torsional rigidity
Topics Gauss curvature flow, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “Minkowski”
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The -th dual Minkowski problem for the -torsional rigidity corresponding to a -Hessian equation
Topics Gauss curvature flow, Other curvature flows · Same authors Xia Zhao, Peibiao Zhao · Shared terms “Minkowski”, “Huang”, “Motivated”
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A Gauss curvature flow related to the Orlicz-Aleksandrov problem
Topics Gauss curvature flow, Other curvature flows · Same author Peibiao Zhao · Shared terms “smooth solutions”
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