Orbifold spectral theory

Abstract

In this paper we study Sobolev spaces for smooth closed orientable Riemannian orbifolds. In particular we prove the Sobolev embedding theorem, the Rellich- Kondrakov theorem and Poincare’s inequalities. From these theorems we derive properties of the spectrum of the Laplacian. In particular, Weil’s asymptotic formula and estimates from below of the eigenvalues of the Laplacian are proved in analogy with the manifold case. © 2001 Rocky Mountain Mathematics Consortium.