2014/03/05 by Jean‐Baptiste Casteras, Jean-Baptiste Casteras, Jaime Ripoll +2
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.DG
paper · pdf · doi:10.48550/arxiv.1403.1160
arxiv created 2014/03/05 · arxiv updated 2014/03/06
Let M be a Hadamard manifold with curvature bounded above by a negative constant -α, satisfying the "strict convexity condition", and assume that M admits a "helicoidal" one-parameter subgroup G of isometries of M. Then, given a compact topological G-shaped hypersurface Γ in the asymptotic boundary of M, and |H|<√α, we prove the existence of a complete properly embedded hypersurface whose mean curvature is equal to H and whose asymptotic boundary is Γ. We are able, this way, to extend a previous theorem of B.Guan and J.Spruck on the hyperbolic space to any rank 1 symmetric spaces of non compact type and to more general boundary data.