2003/01/30 by Elizabeth Stanhope, Stanhope, Elizabeth
Mathematics · #53C20 #58J50 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #Spectral Theory (math.SP) #math.DG #math.SP #msc:53C20 #msc:58J50
paper · pdf · doi:10.48550/arxiv.math/0301357
20 pages, 6 figures
arxiv created 2003/01/30 · openalex publication_date 2003/01/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We first show that a Laplace isospectral family of Riemannian orbifolds, satisfying a lower Ricci curvature bound, contains orbifolds with points of only finitely many isotropy types. If we restrict our attention to orbifolds with only isolated singularities, and assume a lower sectional curvature bound, then the number of singular points in an orbifold in such an isospectral family is universally bounded above. These proofs employ spectral theory methods of Brooks, Perry and Petersen, as well as comparison geometry techniques developed by Grove and Petersen.