Uniqueness Results of Algebraic Curves and Related Topics

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dc.contributor.advisorRu, Min
dc.contributor.committeeMemberHeier, Gordon
dc.contributor.committeeMemberJi, Shanyu
dc.contributor.committeeMemberFeng, Qianmei
dc.creatorKaymanli, Gul Ugur 1985-
dc.creator.orcid0000-0003-4932-894X
dc.date.accessioned2017-07-05T21:05:40Z
dc.date.available2017-07-05T21:05:40Z
dc.date.createdMay 2017
dc.date.issued2017-05
dc.date.submittedMay 2017
dc.date.updated2017-07-05T21:05:41Z
dc.description.abstractIt is well-known that if two complex polynomials P and Q share two values without counting multiplicities, then they are the same. Such problem is called the value sharing problem. In this dissertation, we study the value sharing problem for algebraic and holomorphic curves, as well as give its applications. We first improve the previous result of Ru-Xu on value sharing for algebraic mappings from a compact Riemann surface into the n-dimensional projective space that agree on the pre-image for given hyperplanes located in general position, by using a new auxiliary function. Second, we study the value sharing problem for holomorphic mappings from punctured compact Riemann surfaces into the n-dimensional projective space. We also work on p-adic holomorphic curves which is similar to the algebraic curves. In the last chapter, we apply our results to the study of minimal surfaces, namely, the uniqueness theorem for Gauss maps of two minimal surfaces in the n-dimensional Euclidean space. The article which contains the majority results of this thesis has been accepted by the International Journal of Mathematics.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginborn digital
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/10657/1866
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.subjectUniqueness theorems
dc.subjectSecond Main Theorem
dc.subjectNevanlinna theory
dc.subjectAlgebraic curves
dc.subjectHolomorphic curves
dc.subjectGauss maps
dc.subjectMinimal surfaces
dc.titleUniqueness Results of Algebraic Curves and Related Topics
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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