Minimal Lagrangian diffeomorphisms between hyperbolic cone surfaces and Anti-de Sitter geometry

Reference : Minimal Lagrangian diffeomorphisms between hyperbolic cone surfaces and Anti-de Sitte...


	Document type :	Scientific Presentations in Universities or Research Centers : Scientific presentation in universities or research centers
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/21785

Title :	Minimal Lagrangian diffeomorphisms between hyperbolic cone surfaces and Anti-de Sitter geometry
Language :	English
Author, co-author :	Toulisse, Jérémy [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Publication date :	13-Jul-2015
Number of pages :	92
Event name :	Thesis defense
Event date :	31/07/2015
Keywords :	[en] Anti-de Sitter geometry ; Cone singularities ; Minimal surfaces ; Harmonic maps ; Maximal surfaces ; Hyperbolic geometry
Abstract :	[en] We study minimal diffeomorphisms between hyperbolic cone-surfaces (that is diffeomor- phisms whose graph are minimal submanifolds). We prove that, given two hyperbolic metrics with the same number of conical singularities of angles less than π, there always exists a minimal diffeomorphism isotopic to the identity. When the cone-angles of one metric are strictly smaller than the ones of the other, we prove that this diffeomorphism is unique. When the angles are the same, we prove that this diffeomorphism is unique and area- preserving (so is minimal Lagrangian). The last result is equivalent to the existence of a unique maximal space-like surface in some Globally Hyperbolic Maximal (GHM) anti-de Sitter (AdS) 3-manifold with particles.
Permalink :	http://hdl.handle.net/10993/21785

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