论文标题
折叠图与非物质弯曲的歧管上的大地测量随机行走相关的地图
Fold maps associated to geodesic random walks on non-positively curved manifolds
论文作者
论文摘要
我们研究了单位切线球的力量的映射家族，即具有非阳性截面曲率的完整riemannian歧管，其行为与球形平均算子和地理随机行动有关。 我们表明，对于单元切线球的奇数功率，映射是折叠图。 讨论了地球随机步行的过渡密度的规律性以及球形平均操作员的本征函数的某些后果，并与先前的工作有关。
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.
