Min-max theory for minimal hypersurfaces with boundary

By Camillo De Lellis, Jusuf Ramic. 2016

48 citations recorded by the source corpus.

In this note we propose a min-max theory for embedded hypersurfaces with a fixed boundary and apply it to prove several theorems about the existence of embedded minimal hypersurfaces with a given boundary. A simpler variant of these theorems holds also for the case of the free boundary minimal surfaces.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/66bb07b90fdd7c1a72e8d465f8fa7d38c57257a7

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Free boundary minimal surfaces in the unit ball : recent advances and open questions (2019, background): “Some recent works related to this include [65] [66] [16] [35] [34] [92] [93].”
Compactness analysis for free boundary minimal hypersurfaces (2017, result): “In more general settings, we shall mention here the results by Li [25], Li-Zhou [26], De LellisRamic [11] and Maximo-Nunes-Smith [27], the former three works extending the min-max theory to the free boundary setting and the latter being based on a degree-theoretic approach.”
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.”
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].”