arXiv:2308.00080 Abstract | arXiv Analytics

arXiv:2308.00080 [math.DG]Abstract References Reviews Resources

Volume of Tubes and Concentration of Measure in Riemannian Geometry

Published 2023-07-31Version 1

We investigate the notion of concentration locus introduced in \cite{CacUrs22}, in the case of Riemann manifolds sequences and its relationship with the volume of tubes. After providing a general formula for the volume of a tube around a Riemannian submanifold of a Riemannian manifold, we specialize it to the case of totally geodesic submanifolds of compact symmetric spaces. In the case of codimension one, we prove explicitly concentration. Then, we investigate for possible characterizations of concentration loci in terms of Wasserstein and Box distances.

Comments: 14 pages

Categories: math.DG, math.GN

Keywords: riemannian geometry, concentration locus, riemann manifolds sequences, compact symmetric spaces, general formula

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