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A Gap Theorem for Free Boundary Minimal Surfaces in Geodesic Balls of Hyperbolic Space and Hemisphere

Li, Haizhong; Xiong, Changwei

Description

In this paper we provide a pinching condition for the characterization of the totally geodesic disk and the rotational annulus among minimal surfaces with free boundary in geodesic balls of three-dimensional hyperbolic space and hemisphere. The pinching condition involves the length of the second fundamental form, the support function of the surface, and a natural potential function in hyperbolic space and hemisphere.

dc.contributor.authorLi, Haizhong
dc.contributor.authorXiong, Changwei
dc.date.accessioned2021-04-28T04:28:34Z
dc.identifier.issn1050-6926
dc.identifier.urihttp://hdl.handle.net/1885/231083
dc.description.abstractIn this paper we provide a pinching condition for the characterization of the totally geodesic disk and the rotational annulus among minimal surfaces with free boundary in geodesic balls of three-dimensional hyperbolic space and hemisphere. The pinching condition involves the length of the second fundamental form, the support function of the surface, and a natural potential function in hyperbolic space and hemisphere.
dc.description.sponsorshipThe first author was supported by NSFC Grant No. 11671224. The second author was supported by a postdoctoral fellowship funded via ARC Laureate Fellowship FL150100126.
dc.format.mimetypeapplication/pdf
dc.language.isoen_AU
dc.publisherAmerican Mathematical Society
dc.rights© Mathematica Josephina, Inc. 2017
dc.sourceJournal of Geometric Analysis
dc.subjectGap theorem
dc.subjectMinimal surface
dc.subjectFree boundary
dc.subjectHyperbolic space
dc.subjectHemisphere
dc.titleA Gap Theorem for Free Boundary Minimal Surfaces in Geodesic Balls of Hyperbolic Space and Hemisphere
dc.typeJournal article
local.description.notesImported from ARIES
local.identifier.citationvolume28
dc.date.issued2017
local.identifier.absfor010112 - Topology
local.identifier.ariespublicationu4351680xPUB464
local.publisher.urlhttp://www.springerlink.com/
local.type.statusAccepted Version
local.contributor.affiliationLi, Haizhong, Tsinghua University
local.contributor.affiliationXiong, Changwei, College of Science, ANU
dc.relationhttp://purl.org/au-research/grants/arc/FL150100126
local.bibliographicCitation.issue4
local.bibliographicCitation.startpage3171
local.bibliographicCitation.lastpage3182
local.identifier.doi10.1007/s12220-017-9953-6
local.identifier.absseo970101 - Expanding Knowledge in the Mathematical Sciences
dc.date.updated2020-11-23T10:05:49Z
local.identifier.scopusID2-s2.0-85032661397
dcterms.accessRightsOpen Access
dc.provenancehttps://v2.sherpa.ac.uk/id/publication/17267..."The Accepted Version can be archived in Institutional Repository" from SHERPA/RoMEO site (as at 30/04/2021).
CollectionsANU Research Publications

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