Some recent developments on Hopf's holomorphic form

DOI10.1007/s00025-011-0150-9zbMath1256.53006OpenAlexW2063181246MaRDI QIDQ1758346

Manfredo Perdigão do Carmo

Publication date: 9 November 2012

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

Full work available at URL: https://doi.org/10.1007/s00025-011-0150-9

zbMATH Keywords

Riemann surfacesconstant mean curvatureHopf-type theoremsHopf's quadratic form

Mathematics Subject Classification ID

Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Cites Work

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• A Hopf differential for constant mean curvature surfaces in \(\mathbb S^2 \times \mathbb R\) and \(\mathbb H^2 \times\mathbb R\)
• A Hopf theorem for ambient spaces of dimensions higher than three
• Counterexample to a conjecture of H. Hopf
• Existence and uniqueness of maps into affine homogeneous spaces
• A theorem of Hopf and the Cauchy-Riemann inequality
• Surfaces with parallel mean curvature vector in $\mathbb{S}^{2}×\mathbb{S}^{2}$ and $\mathbb{H}^{2}×\mathbb{H}^{2}$
• An Elementary Proof of the Existence of Isothermal Parameters on a Surface
• Submanifolds with Constant Mean Curvature
• SURFACES WITH CONSTANT MEAN CURVATURE IN RIEMANNIAN PRODUCTS
• Über Flächen mit einer Relation zwischen den Hauptkrümmungen. Meinem Lehrer Erhard Schmidt in Verehrung und Freundschaft zum 75. Geburtstag gewidmet.

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