Minimal surfaces in pseudohermitian geometry

Jih-Hsin Cheng; Jenn-Fang Hwang; Andrea Malchiodi; Paul Yang

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Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the $(2, 3)$ case

Nataliya Shcherbakova (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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We study minimal surfaces in sub-riemannian manifolds with sub-riemannian structures of co-rank one. These surfaces can be defined as the critical points of the so-called horizontal area functional associated with the canonical horizontal area form. We derive the intrinsic equation in the general case and then consider in greater detail $2$ -dimensional surfaces in contact manifolds of dimension $3$ . We show that in this case minimal surfaces are projections of a special class of $2$ -dimensional...

Some recent developments in the theory of properly embedded minimal surfaces in $ℝ^{3}$

Harold Rosenberg (1991-1992)

Séminaire Bourbaki

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Nonparametric minimal surfaces in $R^{3}$ whose boundaries have a jump discontinuity.

Lancaster, Kirk E. (1988)

International Journal of Mathematics and Mathematical Sciences

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Curvature estimates for minimal surfaces in $3$ -manifolds

Michael T. Anderson (1985)

Annales scientifiques de l'École Normale Supérieure

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Complete classification of surfaces with a canonical principal direction in the Euclidean space $𝔼$ 3

Marian Munteanu, Ana Nistor (2011)

Open Mathematics

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In the present paper we classify all surfaces in $𝔼$ 3 with a canonical principal direction. Examples of this type of surfaces are constructed. We prove that the only minimal surface with a canonical principal direction in the Euclidean space $𝔼$ 3 is the catenoid.

A limiting geometry for capillary surfaces

Robert Finn (1984)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Displaying similar documents to “Minimal surfaces in pseudohermitian geometry”

Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the ( 2 , 3 ) case

Some recent developments in the theory of properly embedded minimal surfaces in ℝ 3

Nonparametric minimal surfaces in R 3 whose boundaries have a jump discontinuity.

Curvature estimates for minimal surfaces in 3 -manifolds

Complete classification of surfaces with a canonical principal direction in the Euclidean space 𝔼 3

A limiting geometry for capillary surfaces

Minimal surfaces in sub-riemannian manifolds and structure of their singular sets in the $(2, 3)$ case

Some recent developments in the theory of properly embedded minimal surfaces in $ℝ^{3}$

Nonparametric minimal surfaces in $R^{3}$ whose boundaries have a jump discontinuity.

Curvature estimates for minimal surfaces in $3$ -manifolds

Complete classification of surfaces with a canonical principal direction in the Euclidean space $𝔼$ 3