2019/05/17 by Tristan Rivière, Rivière, Tristan
Mathematics · #49Q05 #49Q20 #53C22 #53C42 #58E05 #58E10 #58Exx #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1905.07120
openalex publication_date 2019/05/17 · openalex created_date 2019/05/29 · openalex updated_date 2026/07/28
A classical result by Marston Morse asserts that on some ellipsoids of \mathbb R3 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.