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Title: In search of minimal hypersurfaces
Authors: Song, Antoine
Advisors: Marques, Fernando C.
Contributors: Mathematics Department
Keywords: minimal surfaces
min-max theory
Subjects: Theoretical mathematics
Issue Date: 2019
Publisher: Princeton, NJ : Princeton University
Abstract: We study minimal hypersurfaces from the point of view of min-max theory. We present a proof of Yau's conjecture for the abundance of minimal surfaces, which builds on previous works by F. C. Marques and A. Neves, and extend it to some non-compact ambient manifolds. We show a generic equidistribution result for minimal hypersurfaces (joint with F. C. Marques and A. Neves). Then we give a proof of a conjecture by H. J. Rubinstein on realizing strongly irreducible Heegaard splittings of $3$-manifolds by minimal surfaces (joint with D. Ketover and Y. Liokumovich). Other results related to minimal surfaces are explained.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: ang
Appears in Collections:Mathematics

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