Dissertation/Thesis Abstract

In Search of Minimal Hypersurfaces
by Song, Antoine, Ph.D., Princeton University, 2019, 208; 13882316
Abstract (Summary)

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.

Indexing (document details)
Advisor: Marques, Fernando C.
Commitee: Gabai, David, Yang, Paul
School: Princeton University
Department: Mathematics
School Location: United States -- New Jersey
Source: DAI-B 80/11(E), Dissertation Abstracts International
Subjects: Theoretical Mathematics
Keywords: Min-max theory, Minimal surfaces
Publication Number: 13882316
ISBN: 978-1-392-26966-4
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