A prescribed Gauss-Kronecker curvature problem on the product of unit spheres
Wang ZhiZhang
TL;DR
This paper investigates the problem of prescribing Gauss-Kronecker curvature on the product of unit spheres, aiming to understand the geometric conditions and solutions for such curvature prescriptions.
Contribution
It introduces a new approach to solving the prescribed Gauss-Kronecker curvature problem specifically on the product of unit spheres, expanding existing geometric analysis methods.
Findings
Established conditions for the existence of solutions
Derived new curvature equations for the product of spheres
Provided examples illustrating the curvature prescription
Abstract
The present paper discusses that a prescribed Gauss-Kronecker curvature problem on the product of unit spheres.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Mathematics and Applications · Analytic and geometric function theory