The Codazzi equation for surfaces

DOI10.1016/j.aim.2010.02.007zbMath1203.53016arXiv0902.2283OpenAlexW1977819893WikidataQ125599424 ScholiaQ125599424MaRDI QIDQ984881

José M. Espinar, José A. Gálvez, Juan A. Aledo

Publication date: 20 July 2010

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0902.2283

zbMATH Keywords

maximum principleHopf differentialWeingarten surfaceCodazzi function

Mathematics Subject Classification ID

Surfaces in Euclidean and related spaces (53A05) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Local submanifolds (53B25) Local Riemannian geometry (53B20)

Related Items (15)

Hypersurfaces with prescribed curvatures in the de Sitter space ⋮ Capillary immersions in \(\mathbb {E}(\kappa , \tau )\) ⋮ Rotational linear Weingarten surfaces into the Euclidean sphere ⋮ Characterization of \(f\)-extremal disks ⋮ Complete surfaces of constant anisotropic mean curvature ⋮ Quasiconformal Gauss maps and the Bernstein problem for Weingarten multigraphs ⋮ Elliptic Weingarten surfaces: singularities, rotational examples and the halfspace theorem ⋮ The global geometry of surfaces with prescribed mean curvature in ℝ³ ⋮ Geometry and topology of some overdetermined elliptic problems ⋮ Ribaucour type transformations for the Hessian one equation ⋮ On higher-order Codazzi tensors on complete Riemannian manifolds ⋮ Height estimate for special Weingarten surfaces of elliptic type in 𝕄²(𝕔)×ℝ ⋮ The Abresch–Rosenberg shape operator and applications ⋮ Hypersurfaces in hyperbolic space with support function ⋮ Complete surfaces with non-positive extrinsic curvature in \(\mathbb{H}^3\) and \(\mathbb{S}^3\)

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