Fold maps associated to geodesic random walks on non-positively curved manifolds
Resumen:
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.
| 2020 | |
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MATHEMATICS - DIFFERENTIAL GEOMETRY MATHEMATICS - PROBABILITY GEODESIC RANDOM WALK SPHERICAL MEAN OPERATOR FOLD MAPS |
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| Inglés | |
| Universidad de la República | |
| COLIBRI | |
| https://hdl.handle.net/20.500.12008/44751 | |
| Acceso abierto | |
| Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| _version_ | 1807522809947095040 |
|---|---|
| author | Lessa Echeverriarza, Pablo |
| author2 | Oliveira, Lucas |
| author2_role | author |
| author_facet | Lessa Echeverriarza, Pablo Oliveira, Lucas |
| author_role | author |
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| collection | COLIBRI |
| dc.contributor.filiacion.none.fl_str_mv | Lessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática. Oliveira Lucas |
| dc.creator.none.fl_str_mv | Lessa Echeverriarza, Pablo Oliveira, Lucas |
| dc.date.accessioned.none.fl_str_mv | 2024-07-15T12:17:43Z |
| dc.date.available.none.fl_str_mv | 2024-07-15T12:17:43Z |
| dc.date.issued.none.fl_str_mv | 2020 |
| dc.description.abstract.none.fl_txt_mv | 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. |
| dc.description.es.fl_txt_mv | Versión permitida preprint. Publicado tambien en: Hokkaido Math. J. 2023, 52(1) : 75-96. DOI: 10.14492/hokmj/2020-439 |
| dc.format.extent.es.fl_str_mv | 11 p. |
| dc.format.mimetype.es.fl_str_mv | application/pdf |
| dc.identifier.citation.es.fl_str_mv | Lessa Echeverriarza, P y Oliveira, L. "Fold maps associated to geodesic random walks on non-positively curved manifolds" [Preprint]. Publicado en: Mathematics (Differential Geometry). 2020, arXiv:2003.07255v1, mar. 2020, pp 1-11 |
| dc.identifier.doi.none.fl_str_mv | 10.48550/arXiv.2003.07255 |
| dc.identifier.uri.none.fl_str_mv | https://hdl.handle.net/20.500.12008/44751 |
| dc.language.iso.none.fl_str_mv | en eng |
| dc.publisher.es.fl_str_mv | arXiv |
| dc.relation.ispartof.es.fl_str_mv | Mathematics (Differential Geometry), arXiv:2003.07255v1, mar. 2020, pp 1-11 |
| dc.rights.license.none.fl_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| dc.rights.none.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.source.none.fl_str_mv | reponame:COLIBRI instname:Universidad de la República instacron:Universidad de la República |
| dc.subject.other.es.fl_str_mv | MATHEMATICS - DIFFERENTIAL GEOMETRY MATHEMATICS - PROBABILITY GEODESIC RANDOM WALK SPHERICAL MEAN OPERATOR FOLD MAPS |
| dc.title.none.fl_str_mv | Fold maps associated to geodesic random walks on non-positively curved manifolds |
| dc.type.es.fl_str_mv | Preprint |
| dc.type.none.fl_str_mv | info:eu-repo/semantics/preprint |
| dc.type.version.none.fl_str_mv | info:eu-repo/semantics/submittedVersion |
| description | Versión permitida preprint. |
| eu_rights_str_mv | openAccess |
| format | preprint |
| id | COLIBRI_f59d6b30409aa41b2c350647046ba9cc |
| identifier_str_mv | Lessa Echeverriarza, P y Oliveira, L. "Fold maps associated to geodesic random walks on non-positively curved manifolds" [Preprint]. Publicado en: Mathematics (Differential Geometry). 2020, arXiv:2003.07255v1, mar. 2020, pp 1-11 10.48550/arXiv.2003.07255 |
| instacron_str | Universidad de la República |
| institution | Universidad de la República |
| instname_str | Universidad de la República |
| language | eng |
| language_invalid_str_mv | en |
| network_acronym_str | COLIBRI |
| network_name_str | COLIBRI |
| oai_identifier_str | oai:colibri.udelar.edu.uy:20.500.12008/44751 |
| publishDate | 2020 |
| reponame_str | COLIBRI |
| repository.mail.fl_str_mv | mabel.seroubian@seciu.edu.uy |
| repository.name.fl_str_mv | COLIBRI - Universidad de la República |
| repository_id_str | 4771 |
| rights_invalid_str_mv | Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0) |
| spelling | Lessa Echeverriarza Pablo, Universidad de la República (Uruguay). Facultad de Ciencias. Centro de Matemática.Oliveira Lucas2024-07-15T12:17:43Z2024-07-15T12:17:43Z2020Lessa Echeverriarza, P y Oliveira, L. "Fold maps associated to geodesic random walks on non-positively curved manifolds" [Preprint]. Publicado en: Mathematics (Differential Geometry). 2020, arXiv:2003.07255v1, mar. 2020, pp 1-11https://hdl.handle.net/20.500.12008/4475110.48550/arXiv.2003.07255Versión permitida preprint.Publicado tambien en: Hokkaido Math. J. 2023, 52(1) : 75-96. DOI: 10.14492/hokmj/2020-439We 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.Submitted by Egaña Florencia (florega@gmail.com) on 2024-07-11T18:44:19Z No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2003.07255v1.pdf: 236613 bytes, checksum: ab4031a338b7381c843a9b794c337e89 (MD5)Approved for entry into archive by Faget Cecilia (lfaget@fcien.edu.uy) on 2024-07-15T11:43:05Z (GMT) No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2003.07255v1.pdf: 236613 bytes, checksum: ab4031a338b7381c843a9b794c337e89 (MD5)Made available in DSpace by Luna Fabiana (fabiana.luna@seciu.edu.uy) on 2024-07-15T12:17:43Z (GMT). No. of bitstreams: 2 license_rdf: 25790 bytes, checksum: 489f03e71d39068f329bdec8798bce58 (MD5) 2003.07255v1.pdf: 236613 bytes, checksum: ab4031a338b7381c843a9b794c337e89 (MD5) Previous issue date: 202011 p.application/pdfenengarXivMathematics (Differential Geometry), arXiv:2003.07255v1, mar. 2020, pp 1-11Las obras depositadas en el Repositorio se rigen por la Ordenanza de los Derechos de la Propiedad Intelectual de la Universidad de la República.(Res. Nº 91 de C.D.C. de 8/III/1994 – D.O. 7/IV/1994) y por la Ordenanza del Repositorio Abierto de la Universidad de la República (Res. Nº 16 de C.D.C. de 07/10/2014)info:eu-repo/semantics/openAccessLicencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)MATHEMATICS - DIFFERENTIAL GEOMETRYMATHEMATICS - PROBABILITYGEODESIC RANDOM WALKSPHERICAL MEAN OPERATORFOLD MAPSFold maps associated to geodesic random walks on non-positively curved manifoldsPreprintinfo:eu-repo/semantics/preprintinfo:eu-repo/semantics/submittedVersionreponame:COLIBRIinstname:Universidad de la Repúblicainstacron:Universidad de la RepúblicaLessa Echeverriarza, PabloOliveira, LucasLICENSElicense.txtlicense.txttext/plain; charset=utf-84267http://localhost:8080/xmlui/bitstream/20.500.12008/44751/5/license.txt6429389a7df7277b72b7924fdc7d47a9MD55CC-LICENSElicense_urllicense_urltext/plain; charset=utf-850http://localhost:8080/xmlui/bitstream/20.500.12008/44751/2/license_urla006180e3f5b2ad0b88185d14284c0e0MD52license_textlicense_texttext/html; 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- Universidad de la Repúblicafalse |
| spellingShingle | Fold maps associated to geodesic random walks on non-positively curved manifolds Lessa Echeverriarza, Pablo MATHEMATICS - DIFFERENTIAL GEOMETRY MATHEMATICS - PROBABILITY GEODESIC RANDOM WALK SPHERICAL MEAN OPERATOR FOLD MAPS |
| status_str | submittedVersion |
| title | Fold maps associated to geodesic random walks on non-positively curved manifolds |
| title_full | Fold maps associated to geodesic random walks on non-positively curved manifolds |
| title_fullStr | Fold maps associated to geodesic random walks on non-positively curved manifolds |
| title_full_unstemmed | Fold maps associated to geodesic random walks on non-positively curved manifolds |
| title_short | Fold maps associated to geodesic random walks on non-positively curved manifolds |
| title_sort | Fold maps associated to geodesic random walks on non-positively curved manifolds |
| topic | MATHEMATICS - DIFFERENTIAL GEOMETRY MATHEMATICS - PROBABILITY GEODESIC RANDOM WALK SPHERICAL MEAN OPERATOR FOLD MAPS |
| url | https://hdl.handle.net/20.500.12008/44751 |
