On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space

Karp, L.; Peyerimhoff, N.

Abstract

Let H be the n-dimensional real hyperbolic space and pi: H -> M be the universal covering map of a compact Riemannian manifold M of constant curvature -1. Let P be a k-dimensional complete totally geodesic submanifold of H and P_r be the corresponding tubular hypersurface at distance r. In this article we prove that pi(P_r) distributes increasingly uniformly in M as r tends to infinity. Using eigenspace decomposition of the Laplacian, this fact can be considered as geometric application of the asymptotics of a particular ordinary differential equation.

Citation

Karp, L., & Peyerimhoff, N. (1998). On the distribution of hypersurfaces equidistant from totally geodesic submanifolds in hyperbolic space. Analysis, 18, 217-225. https://doi.org/10.1524/anly.1998.18.3.217

• Journal Article Type: Article
• Publication Date: 1998
• Journal: Analysis: International mathematical journal of analysis and its applications
• Print ISSN: 0174-4747
• Electronic ISSN: 0174-4747
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 18
• Pages: 217-225
• DOI: https://doi.org/10.1524/anly.1998.18.3.217