Polygonal surfaces in pseudo-hyperbolic spaces

Appears in collection : 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

A polygonal surface in the pseudo-hyperbolic space is a complete maximal surface bounded by a lightlike polygon with finitely many vertices. Among maximal surfaces, polygonal surfaces admit several characterizations : being asymptotically flat or having finite total curvature. In this talk we will explain some constructions coming from nonpositive curvature geometry to prove the equivalence, for a maximal surface, between being polygonal and having finite total curvature.

Information about the video

Date of recording 21/05/2025
Date of publication 21/05/2025
Institution IHP
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Hermite Amphitheater

Domain(s)

Geometric Topology

Bibliography

Moriani "Polygonal surfaces in pseudo-hyperbolic spaces"
Labourie-Toulisse-Wolf "Plateau Problems for Maximal Surfaces in Pseudo-Hyperbolic Spaces"
Tamburelli "Polynomial quadratic differentials on the complex plane and light-like polygons in the Einstein Universe"
Tamburelli-Wolf "Planar minimal surfaces with polynomial growth in the Sp(4,R)-symmetric space"