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.
Acknowledgment
The author's would like to thank Gilles Courtois, Rafael Potrie, Martin Reiris, and Rafael Ruggiero for their help. Both authors would also like to thank the anonymous referee, whose detailed comments helped improve this work.
Citation
Pablo LESSA. Lucas OLIVEIRA. "Fold maps associated to geodesic random walks on non-positively curved manifolds." Hokkaido Math. J. 52 (1) 75 - 96, February 2023. https://doi.org/10.14492/hokmj/2020-439
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