  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.

Differential Geometry