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In Search of Minimal Hypersurfaces.

Song, Antoine.

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In Search of Minimal Hypersurfaces.

Record Type:	Electronic resources : Monograph/item
Title/Author:	In Search of Minimal Hypersurfaces./
Author:	Song, Antoine.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	208 p.
Notes:	Source: Dissertations Abstracts International, Volume: 81-01, Section: B.
Contained By:	Dissertations Abstracts International81-01B.
Subject:	Theoretical mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13882316
ISBN:	9781392269664

In Search of Minimal Hypersurfaces.
Song, Antoine.

In Search of Minimal Hypersurfaces. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 208 p.

Source: Dissertations Abstracts International, Volume: 81-01, Section: B.

Thesis (Ph.D.)--Princeton University, 2019.

This item must not be sold to any third party vendors.

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.

ISBN: 9781392269664Subjects--Topical Terms:

3173530
Theoretical mathematics.

In Search of Minimal Hypersurfaces.
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020 $a 9781392269664
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100 1 $a Song, Antoine. $3 3437962
245 1 0 $a In Search of Minimal Hypersurfaces.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 208 p.
500 $a Source: Dissertations Abstracts International, Volume: 81-01, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Marques, Fernando C.
502 $a Thesis (Ph.D.)--Princeton University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a 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.
590 $a School code: 0181.
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710 2 $a Princeton University. $b Mathematics. $3 2049791
773 0 $t Dissertations Abstracts International $g 81-01B.
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791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13882316