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Mean curvature, volume and properness of isometric immersions
dc.contributor.author | Gimeno, Vicent | |
dc.contributor.author | Palmer Andreu, Vicente | |
dc.date.accessioned | 2017-06-12T17:45:09Z | |
dc.date.available | 2017-06-12T17:45:09Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | GIMENO, Vicent; PALMER, Vicente. Mean curvature, volume and properness of isometric immersions. Transactions of the American Mathematical Society, 2017, vol. 369, no 6, p. 4347-4366 | ca_CA |
dc.identifier.issn | 1088-6850 | |
dc.identifier.issn | 0002-9947 | |
dc.identifier.uri | http://hdl.handle.net/10234/1T67961 | |
dc.description.abstract | We explore the relation among volume, curvature and properness of an m -dimensional isometric immersion in a Riemannian manifold. We show that, when the L p -norm of the mean curvature vector is bounded for some m ≤ p ≤∞ , and the ambient manifold is a Riemannian manifold with bounded geometry, properness is equivalent to the finiteness of the volume of extrinsic balls. We also relate the total absolute curvature of a surface isometrically immersed in a Riemannian manifold with its properness. Finally, we relate the curvature and the topology of a complete and non-compact 2-Riemannian manifold M with non-positive Gaussian curvature and finite topology, using the study of the focal points of the transverse Jacobi fields to a geodesic ray in M . In particular, we have explored the relation between the minimal focal distance of a geodesic ray and the total curvature of an end containing that geodesic ray. | ca_CA |
dc.description.sponsorShip | The first author’s work was partially supported by the Research Program of University Jaume I Project P1-1B2012-18, and DGI -MINECO grant (FEDER) MTM2013-48371-C2-2-P. The second author’s work was partially supported by the Research Program of University Jaume I Project P1-1B2012-18, DGI -MINECO grant (FEDER) MTM2013-48371-C2-2-P, and Generalitat Valenciana Grant PrometeoII/2014/064 . | ca_CA |
dc.format.extent | 20 p. | ca_CA |
dc.format.mimetype | application/pdf | ca_CA |
dc.language.iso | eng | ca_CA |
dc.publisher | American Mathematical Society | ca_CA |
dc.relation.isPartOf | Transactions of the American Mathematical Society, 2017, vol. 369, núm. 6 | ca_CA |
dc.rights | © 2017 American Mathematical Society. First published in Proceedings of the American Mathematical Society in volume 369, number 6, June 2017, published by the American Mathematical Society. | ca_CA |
dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | * |
dc.subject | Focal distance | ca_CA |
dc.subject | Geodesic ray | ca_CA |
dc.subject | Total curvature | ca_CA |
dc.subject | Properness | ca_CA |
dc.subject | Calabi's conjecture | ca_CA |
dc.title | Mean curvature, volume and properness of isometric immersions | ca_CA |
dc.type | info:eu-repo/semantics/article | ca_CA |
dc.identifier.doi | https://doi.org/10.1090/tran/6892 | |
dc.rights.accessRights | info:eu-repo/semantics/restrictedAccess | ca_CA |
dc.relation.publisherVersion | http://www.ams.org/journals/tran/2017-369-06/S0002-9947-2017-06892-6/ | ca_CA |
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