Prescription of Gauss curvature on compact hyperbolic orbifolds
Copyright policy )Prescription of Gauss curvature on compact hyperbolic orbifolds
This paper is organized in the following way: Section 1 contains preliminaries and the problem of prescribing the Gauss curvature of convex sets in the Minkowski spacetime, which is a generalization of a result by Alexandrov for Euclidean convex bodies. The model of the duality of star-shaped sets in the Minkowski spacetime is presented in Section 2. Section 3. Equivalence of Theorem 1.3 and Theorem 1.4. The solutions of both problems are in one-to-one correspondence. The main result of this paper is given by Theorem (1.3). Reviewer's remark: The general theory of the Gauss curvature prescription is given by Kazdan's theory.
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Gauss curvature, 530, Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry), 510, optimal mass transport, Variational problems in a geometric measure-theoretic setting, Convex bodies, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], convex bodies, [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]
Differential geometry of immersions (minimal, prescribed curvature, tight, etc.), Gauss curvature, 530, Lattices and convex bodies in \(n\) dimensions (aspects of discrete geometry), 510, optimal mass transport, Variational problems in a geometric measure-theoretic setting, Convex bodies, [MATH.MATH-MG] Mathematics [math]/Metric Geometry [math.MG], convex bodies, [MATH.MATH-MG]Mathematics [math]/Metric Geometry [math.MG]
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