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dc.contributor.authorMarkvorsen, Steen
dc.contributor.authorPalmer Andreu, Vicente
dc.date.accessioned2013-07-09T17:37:22Z
dc.date.available2013-07-09T17:37:22Z
dc.date.issued2010
dc.identifier.citationJournal of Geometric Analysis April 2010, Volume 20, Issue 2, pp 388-421ca_CA
dc.identifier.issn1050-6926
dc.identifier.issn1559-002X
dc.identifier.urihttp://hdl.handle.net/10234/70100
dc.description.abstractWe obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on the radial part of the mean curvature vector field and on the radial part of the intrinsic unit normals at the boundaries of the extrinsic spheres, respectively. In the same vein we also establish lower bounds on the mean exit time for Brownian motions in the extrinsic balls, i.e. lower bounds for the time it takes (on average) for Brownian particles to diffuse within the extrinsic ball from a given starting point before they hit the boundary of the extrinsic ball. In those cases, where we may extend our analysis to hold all the way to infinity, we apply a capacity comparison technique to obtain a sufficient condition for the submanifolds to be parabolic, i.e. a condition which will guarantee that any Brownian particle, which is free to move around in the whole submanifold, is bound to eventually revisit any given neighborhood of its starting point with probability 1. The results of this paper are in a rough sense dual to similar results obtained previously by the present authors in complementary settings where we assume that the curvatures are bounded from above.ca_CA
dc.format.extent39 p.ca_CA
dc.format.mimetypeapplication/pdfca_CA
dc.language.isoengca_CA
dc.publisherSpringer Verlagca_CA
dc.relation.isPartOfJournal of Geometric Analysis, 2010, vol. 20, num. 2ca_CA
dc.rights© Springer, Part of Springer Science+Business Media. The final publication is available at link.springer.comca_CA
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/*
dc.subjectSubmanifoldsca_CA
dc.subjectExtrinsic ballsca_CA
dc.subjectRadial convexityca_CA
dc.subjectRadial tangencyca_CA
dc.subjectMean exit timeca_CA
dc.subjectIsoperimetric inequalitiesca_CA
dc.subjectVolume boundsca_CA
dc.subjectParabolicityca_CA
dc.subject53C42ca_CA
dc.subject58J65ca_CA
dc.subject35J25ca_CA
dc.subject60J65ca_CA
dc.titleExtrinsic isoperimetric analysis on submanifolds with curvatures bounded from belowca_CA
dc.typeinfo:eu-repo/semantics/articleca_CA
dc.identifier.doihttp://dx.doi.org/10.1007/s12220-009-9111-x
dc.rights.accessRightsinfo:eu-repo/semantics/openAccessca_CA
dc.relation.publisherVersionhttp://link.springer.com/article/10.1007%2Fs12220-009-9111-xca_CA
dc.type.versioninfo:eu-repo/semantics/acceptedVersion


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