2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Collection 2025 - T2 - WS1 - Higher rank geometric structures, Higgs bundles and physics

Organizer(s) Canary, Richard ; Garcia-Faide, Elba ; Labourie, François ; Li, Qiongling ; Neitzke, Andrew ; Pozzetti, Beatrice ; Wienhard, Anna
Date(s) 19/05/2025 - 27/05/2025
linked URL https://indico.math.cnrs.fr/event/11569/
9 20

Polygonal surfaces in pseudo-hyperbolic spaces

By Alex Moriani

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.

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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"

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