Thickness Formula and C^1-Compactness for C^{1,1} Riemannian Submanifolds
Differential Geometry
2016-09-07 v1 Geometric Topology
Abstract
We prove a formula for the normal injectivity radius(thickness)i(K,M)for C^{1,1} compact submanifolds K^k of complete Riemannian manifolds M^n in terms of geometric focal distance and double critical points. We also prove the C^1 compactness of the set of all compact submanifolds K contained in a compact subset D of a fixed manifold M with i(K,M) bounded away from 0. This is an extrinsic and isometric embeddindg type theorem related to Gromov's compactness theorem. This yields the existence of thickest submanifolds in an isotopy class where K is not necessarily connected.
Keywords
Cite
@article{arxiv.math/0204050,
title = {Thickness Formula and C^1-Compactness for C^{1,1} Riemannian Submanifolds},
author = {O. C. Durumeric},
journal= {arXiv preprint arXiv:math/0204050},
year = {2016}
}