Fold maps associated to geodesic random walks on non-positively curved manifolds

2020/03/16 by Pablo Lessa, Lessa, Pablo, Lucas Oliveira +1
Mathematics · #53C22 #57R45 #60J10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Morphological variations and asymmetry #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2003.07255

openalex publication_date 2020/03/16 · openalex created_date 2023/07/11 · openalex updated_date 2026/07/28

Abstract

We study a family of mappings from the powers of the unit tangent sphere at a point to a complete Riemannian manifold with non-positive sectional curvature, whose behavior is related to the spherical mean operator and the geodesic random walks on the manifold. We show that for odd powers of the unit tangent sphere the mappings are fold maps. Some consequences on the regularity of the transition density of geodesic random walks, and on the eigenfunctions of the spherical mean operator are discussed and related to previous work.

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