Thickness Formula and C^1-Compactness for C^{1,1} Riemannian Submanifolds
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Publication:6471770
arXivmath/0204050MaRDI QIDQ6471770
Publication date: 3 April 2002
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.
Global submanifolds (53C40) Global Riemannian geometry, including pinching (53C20) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23)
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