The existence of embedded minimal hypersurfaces

By Camillo De Lellis, Dominik Tasnady. 2009

57 citations recorded by the source corpus.

We give a shorter proof of the existence of nontrivial closed minimal hypersurfaces in closed smooth (n + 1)-dimensional Riemannian manifolds, a theorem proved first by Pitts for 2 ≤ n ≤ 5 and extended later by Schoen and Simon to any n.

View Paper: https://www.semanticscholar.org/paper/c3e48f769e2b5857fb846df5b4f37e679ce27eab

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Citations in the corpus

Min-max theory for minimal hypersurfaces with boundary (2016, methodology): “Our min-max constructions use the simpler and less technical framework proposed by the first author and Tasnady in [10], which is essentially a variant of that developed by Pitts in his groundbreaking monograph [27].”
Min-max for phase transitions and the existence of embedded minimal hypersurfaces (2015, methodology): “When n > 3, a similar refinement of the work of Almgren-Pitts is presented by De Lellis-Tasnady [8].”
Existence of hypersurfaces with prescribed mean curvature I – generic min-max (2018, background): “Consequently, the min-max program has seen a series of developments in various directions, including (but not limited to) [16, 28, 37, 44, 42, 15, 41, 36, 12, 46, 57].”
On the Multiplicity One Conjecture in min-max theory (2019, unknown): “We refer to [39, 6, 10, 17, 9, 23, 7, 47, 50, 32] for other variants of this theory.”
Min-max theory for free boundary minimal hypersurfaces, I: Regularity theory (2016, unknown): “dimensions (see for example [40] [8] [24] [13] [12] [9]).”
Morse index of multiplicity one min-max minimal hypersurfaces (2015, unknown): “It would be interesting to know if similar index bounds hold in other min-max constructions (e.g. ChambersLiokumovich [8], De Lellis-Ramic [11], De Lellis-Tasnady [12], Li-Zhou [27], Montezuma [39]-[40], Zhou-Zhu [64]).”