Smoothing 3-dimensional polyhedral spaces

Abstract

We show that 3-dimensional polyhedral manifolds with nonnegative curvature in the sense of Alexandrov can be approximated by nonnegatively curved 3-dimensional Riemannian manifolds.

7 pages, 1 figure

References in corpus (3)

• Polyhedral approximations of Riemannian manifolds
• Ricci flow of almost non-negatively curved three manifolds
• ${\mathsf{S}}^1$-actions on $4$-manifolds and fixed point homogeneous manifolds of nonnegative curvature

Cited by in corpus (3)

• Ricci flow from spaces with isolated conical singularities
• The large scale structure of complete $4$-manifolds with nonnegative Ricci curvature and Euclidean volume growth
• Singular vertices of nonnegatively curved integral polyhedral 3-manifolds