Year: 2020
Type: preprint
Abstract: We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the pseudo-hyperbolic space which are limits of positive curves. We also discuss a compact Plateau problem. The required compactness arguments rely on an analysis of the pseudo-holomorphic curves defined by the Gauss lifts of the maximal surfaces.
Source: arXiv (Cornell University)
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: RNMS: Geometric structures and representation varieties, G202495085, Geometric Variational Problems in Classical and Higher Rank Teichmuller theory, G471867726, G4929423962, G5148239254, G5636327458, FRG: Collaborative Research: Geometric Structures of Higher Teichmuller Spaces, G5969482202, RNMS: Geometric Structures and Representation Varieties, G7695612773, G7908957721, Mathematical Sciences Research Institute (MSRI), RNMS: Geometric Structures and Representation Varieties
OpenAlex ID: W3036093268