Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature

IF 0.6 3区数学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Discrete & Computational Geometry Pub Date : 2024-07-25 DOI:10.1007/s00454-024-00657-7

Misha Gromov

引用次数: 0

Abstract

We approximate boundaries of convex polytopes \(X\subset {\mathbb {R}}^n\) by smooth hypersurfaces \(Y=Y_\varepsilon \) with positive mean curvatures and, by using basic geometric relations between the scalar curvatures of Riemannian manifolds and the mean curvatures of their boundaries, establish lower bound on the dihedral angles of X.

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凸多边形、二面角、平均曲率和标量曲率

我们用具有正平均曲率的光滑超曲面 \(Y=Y_\varepsilon \)来近似凸多面体 \(X\subset {\mathbb {R}}^n\) 的边界，并利用黎曼流形的标量曲率与其边界的平均曲率之间的基本几何关系，建立 X 的二面角下限。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete & Computational Geometry 数学-计算机：理论方法

CiteScore

1.80

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： Discrete & Computational Geometry (DCG) is an international journal of mathematics and computer science, covering a broad range of topics in which geometry plays a fundamental role. It publishes papers on such topics as configurations and arrangements, spatial subdivision, packing, covering, and tiling, geometric complexity, polytopes, point location, geometric probability, geometric range searching, combinatorial and computational topology, probabilistic techniques in computational geometry, geometric graphs, geometry of numbers, and motion planning.