3 papers
math.DG2024
The Weyl problem for unbounded convex domains in $\HH^3$
Jean-Marc Schlenker
Let $K\subset \HH^3$ be a convex subset in $\HH^3$ with smooth, strictly convex boundary. The induced metric on then has curvature . It was proved by Alexandrov…
math.DG2024
On the Weyl problem for complete surfaces in the hyperbolic and anti-de Sitter spaces
Jean-Marc Schlenker
The classical Weyl problem (solved by Lewy, Alexandrov, Pogorelov, and others) asks whether any metric of curvature on the sphere is induced on the boundary of a unique c…
math.DG2024
The geometric data on the boundary of convex subsets of hyperbolic manifolds
Qiyu Chen, Jean-Marc Schlenker
Let be a geodesically convex subset in a convex co-compact hyperbolic manifold with incompressible boundary. We assume that each boundary component of is either a bound…