Unicity Results for Gauss Maps of Minimal Surfaces Immersed in R^m

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dc.contributor.advisorRu, Min
dc.contributor.committeeMemberJi, Shanyu
dc.contributor.committeeMemberHeier, Gordon
dc.contributor.committeeMemberFeng, Qianmei
dc.creatorPark, Jungim 1972-
dc.creator.orcid0000-0002-4213-6446
dc.date.accessioned2018-11-30T21:16:51Z
dc.date.available2018-11-30T21:16:51Z
dc.date.createdAugust 2016
dc.date.issued2016-08
dc.date.submittedAugust 2016
dc.date.updated2018-11-30T21:16:51Z
dc.description.abstractThe purpose of this dissertation is to discuss the theory of holomorphic curves in order to study value distributions of (generalized) Gauss maps of complete minimal surfaces immersed in R^m. The study was initiated by S.S. Chern and R. Osserman in the 1960s. Since then, it has been developed by F. Xavier, H. Fujimoto, M. Ru, etc. In this dissertation, we prove a unicity theorem for two conformally diffeomorphic complete minimal surfaces immersed in R^m whose generalized Gauss maps f and g agree on the pre-image ⋃_{j=1}^q f^{-1}(H_j) for given hyperplanes H_j (1≤ j ≤ q) in P^{m-1}(C) located in general position, under the assumption that ⋂_{j=1}^{k+1} f^{-1}(H_{i_j}) = ∅. In the case when k=m-1, the result obtained gives an improvement of the earlier result of Fujimoto [13].
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10657/3551
dc.language.isoeng
dc.rightsThe author of this work is the copyright owner. UH Libraries and the Texas Digital Library have their permission to store and provide access to this work. Further transmission, reproduction, or presentation of this work is prohibited except with permission of the author(s).
dc.subjectUnicity Theorem
dc.subjectGauss maps
dc.subjectMinimal surfaces
dc.subjectHyperplanes
dc.subjectComplex geometry
dc.titleUnicity Results for Gauss Maps of Minimal Surfaces Immersed in R^m
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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