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Norbert Peyerimhoff

Spherical means on compact locally symmetric spaces of non-positive curvature

We consider spherical means of continuous functions on the unit tangent bundle of a compact, non-positively curved locally symmetric space and study their behavior as the radius tends to infinity. In dimension ≥ 2, we prove that spherical means converge to a probability measure of maximal entropy (Theorem 1). This limit measure has an easy characterization in both geometric and algebraic terms. On our way we also derive a convergence result for horospherical means on compact locally symmetric spaces of noncompact type (Theorem 3).

Forum Mathematicum, Walter de Gruyter

Print ISSN: 0933-7741
Volume: 18, 05/2006
Pages: 391 - 417

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