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引用次数: 0
摘要
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。
Convex Polytopes, Dihedral Angles, Mean Curvature and Scalar Curvature
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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