Existence of infinitely many minimal hypersurfaces in low dimensions, after F.C. Marques, A.A. Neves et A. Song (Bourbaki Seminar)
A classical result by Marston Morse asserts that on some ellipsoids of ${\mathbb R}^3$ there exists exactly 3 closed and simple geodesics. The goal of this presentation is to prove that this rigidity result does not extend to higher dimensions and, more precisely, on any smooth closed riemannian man...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | A classical result by Marston Morse asserts that on some ellipsoids of
${\mathbb R}^3$ there exists exactly 3 closed and simple geodesics. The goal of
this presentation is to prove that this rigidity result does not extend to
higher dimensions and, more precisely, on any smooth closed riemannian manifod
of arbitrary dimension between 3 and 7 there exists infinitely many closed
embedded minimal surfaces. We are going to present the origins of this theorem
as well as it's proof given recently by Antoine Song. |
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| DOI: | 10.48550/arxiv.1905.07120 |