Please use this identifier to cite or link to this item: http://arks.princeton.edu/ark:/88435/dsp01h128nh572
 Title: In search of minimal hypersurfaces Authors: Song, Antoine Advisors: Marques, Fernando C. Contributors: Mathematics Department Keywords: minimal surfacesmin-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. URI: http://arks.princeton.edu/ark:/88435/dsp01h128nh572 Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu Type of Material: Academic dissertations (Ph.D.) Language: ang Appears in Collections: Mathematics