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Yang-Mills heatflow on gauged holomorphic maps
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Venugopalan, Sushmita. Yang-Mills heatflow on gauged holomorphic maps. Retrieved from https://doi.org/doi:10.7282/T35X27Q1

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TitleYang-Mills heatflow on gauged holomorphic maps
NameVenugopalan, Sushmita (author); Woodward, Chris (chair); Goodman, Roe (internal member); Sesum, Natasa (internal member); Gonzalez, Eduardo (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2012
Other Date2012-10 (degree)
SubjectMathematics, Yang-Mills theory, Domains of holomorphy
Extentv, 76 p. : ill.
DescriptionWe study the gradient flow lines of a Yang-Mills-type functional on the space of gauged holomorphic maps whose domain is a principal bundle on a Riemann surface and the target is a Kahler Hamiltonian manifold. When the Riemann surface in the domain is compact, possibly with boundary, we prove long time existence of the gradient flow. The flow lines converge to critical points of the functional. So, there is a stratification of the space of gauged holomorphic maps that is invariant under the action of the complexified gauge group. Symplectic vortices are the zeros of the functional we study. When the Riemann surface has boundary, similar to Donaldson's result for the Hermitian Yang-Mills equations, we show that there is only a single stratum - any gauged-holomorphic map can be complex gauge transformed to a symplectic vortex. This is a version of Mundet's Hitchin-Kobayashi result on a surface with boundary.
NotePh.D.
NoteIncludes bibliographical references
Noteby Sushmita Venugopalan
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T35X27Q1
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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