Spectral bounds on orbifold isotropy

Details Spectral bounds on orbifold isotropy Spectral bounds on orbifold isotropy

2003-01-30

arxiv.org/abs/math/0301357v1

Mathematics

Spectral Theory

20 pages, 6 figures

Scientific paper

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.

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