{"title":"非正弯曲流形上与测地随机游动相关的折叠映射","authors":"Pablo Lessa, L. Oliveira","doi":"10.14492/hokmj/2020-439","DOIUrl":null,"url":null,"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. \nWe show that for odd powers of the unit tangent sphere the mappings are fold maps. \nSome 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.","PeriodicalId":55051,"journal":{"name":"Hokkaido Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fold maps associated to geodesic random walks on non-positively curved manifolds\",\"authors\":\"Pablo Lessa, L. Oliveira\",\"doi\":\"10.14492/hokmj/2020-439\",\"DOIUrl\":null,\"url\":null,\"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. \\nWe show that for odd powers of the unit tangent sphere the mappings are fold maps. \\nSome 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.\",\"PeriodicalId\":55051,\"journal\":{\"name\":\"Hokkaido Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Hokkaido Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.14492/hokmj/2020-439\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Hokkaido Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14492/hokmj/2020-439","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Fold maps associated to geodesic random walks on non-positively curved manifolds
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.
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.