Spectral and geometric bounds on 2-orbifold diffeomorphism type

Details Spectral and geometric bounds on 2-orbifold diffeomorphism type Spectral and geometric bounds on 2-orbifold diffeomorphism type

2008-11-05

arxiv.org/abs/0811.0797v2

Mathematics

Differential Geometry

Exposition clarified, typographical errors corrected

Scientific paper

We show that a Laplace isospectral family of two dimensional Riemannian orbifolds, sharing a lower bound on sectional curvature, contains orbifolds of only a finite number of orbifold category diffeomorphism types. We also show that orbifolds of only finitely many orbifold diffeomorphism types may arise in any collection of 2-orbifolds satisfying lower bounds on sectional curvature and volume, and an upper bound on diameter. An argument converting spectral data to geometric bounds shows that the first result is a consequence of the second.

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