A Morse lemma for convex surfaces

DOI10.1007/s002220000069zbMath0981.52002arXivmath/9907051OpenAlexW3100194967MaRDI QIDQ1579076

François Labourie

Publication date: 7 March 2002

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9907051

zbMATH Keywords

negative curvaturePlateau problemMorse lemma

Mathematics Subject Classification ID

Foliations in differential topology; geometric theory (57R30) Convex sets in (3) dimensions (including convex surfaces) (52A15)

Related Items (18)

Möbius Structures, Hyperbolic Ends and k-Surfaces in Hyperbolic Space ⋮ The Plateau problem for convex curvature functions ⋮ Special Lagrangian curvature ⋮ The infimum of the dual volume of convex cocompact hyperbolic 3-manifolds ⋮ Clifford structures, bilegendrian surfaces, and extrinsic curvature ⋮ On the asymptotic geometry of finite-type \(k\)-surfaces in three-dimensional hyperbolic space ⋮ On quasicomplete k$k$‐surfaces in 3‐dimensional space‐forms ⋮ Moduli of flat conformal structures of hyperbolic type ⋮ The Dirichlet problem for constant mean curvature graphs in \(\mathbb M\times\mathbb R\) ⋮ Compactness for immersions of prescribed Gaussian curvature. II: Geometric aspects ⋮ Compactness results for immersions of prescribed Gaussian curvature. I: Analytic aspects ⋮ Constant scalar curvature hypersurfaces in \((3 + 1)\)-dimensional GHMC Minkowski spacetimes ⋮ The non-linear Plateau problem in non-positively curved manifolds ⋮ Pointed $k$-surfaces ⋮ Equivariant Plateau problems ⋮ On an Enneper-Weierstrass-type representation of constant Gaussian curvature surfaces in 3-dimensional hyperbolic space ⋮ Higher rank hyperbolicity ⋮ Hyperbolic Plateau problems

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