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oai:www.ideals.illinois.edu:2142/44328 2023-07-11 col_2142_5131 col_2142_16340 com_2142_5130 com_2142_16339 com_2142_8903

Bradlow, Steven B. Kerman, Ely Kirr, Eduard-Wilhelm Bradlow, Steven B. La Nave, Gabriele Liu, Chih-Chung 2013-05-24T22:07:57Z 2013-05-24T22:07:57Z 2013-05 2013-05-24T22:07:57Z 2013-05 "We study vortex equations with a parameter $s$ on smooth vector bundles $E$ over compact K\""ahler manifolds $M$. For each $s$, we invoke techniques in \cite{Br} by turning vortex equations into the elliptic partial differential equations considered in \cite{kw} and obtain a family of solutions. Our results show that away from a singular set, such a family exhibit well controlled convergent behaviors, leading us to prove conjectures posed by Baptista in \cite{Ba} concerning dynamic behaviors of vortices. These results are published in \cite{Li}. We also analyze the analytic singularities on the singular set. The analytic singularities of the PDE's reflect topological inconsistencies as $s \to \infty$. On the second part of the thesis, we form a modification of the limiting objects, leading to a phenomenon of energy concentration known as the ""bubbling"". We briefly survey the established bubbling results in literature." Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2013-03-29T15:37:31Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 5 Liu_Chih-Chung.pdf: 568722 bytes, checksum: a534f68eececa0509ed158fe8f81021d (MD5) Liu_Chih-Chung.pdf: 568722 bytes, checksum: a534f68eececa0509ed158fe8f81021d (MD5) Liu_Chih-Chung.pdf: 568722 bytes, checksum: a534f68eececa0509ed158fe8f81021d (MD5) Liu_Chih-Chung.tex: 226665 bytes, checksum: 50159e7a30c808ba03bc2f0b5bd7a0ce (MD5) Liu_Chih-Chung.pdf: 568722 bytes, checksum: a534f68eececa0509ed158fe8f81021d (MD5) Made available in DSpace on 2013-05-24T22:07:57Z (GMT). No. of bitstreams: 2 Chih-Chung_Liu.pdf: 569546 bytes, checksum: e73054042a16e00eaa658a004e9991ac (MD5) license.txt: 4062 bytes, checksum: a5d45d082183352846d80dd9755b76c8 (MD5) http://hdl.handle.net/2142/44328 en Copyright 2013 Chih-Chung Liu Vortex Equations Mathematical Physics L^2 Geometry Differential Geometry. The analytic and asymptotic behaviors of vortices text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD