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

IF 0.6 4区 数学 Q3 MATHEMATICS
Pablo Lessa, L. Oliveira
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引用次数: 0

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.
非正弯曲流形上与测地随机游动相关的折叠映射
研究了从单位切线球在一点上的幂到具有非正截面曲率的完全黎曼流形的一系列映射,其性质与球面平均算子和流形上的测地线随机游走有关。我们证明了单位切球的奇次映射是折叠映射。讨论了对测地线随机游走的转移密度的规律性和球面平均算子的特征函数的一些结果,并与前人的工作相联系。
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来源期刊
CiteScore
1.00
自引率
0.00%
发文量
14
审稿时长
>12 weeks
期刊介绍: The main purpose of Hokkaido Mathematical Journal is to promote research activities in pure and applied mathematics by publishing original research papers. Selection for publication is on the basis of reports from specialist referees commissioned by the editors.
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