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We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.

Local monotonicity of Hausdorff measures restricted to curves in $ℝ^{n}$

Robert Černý (2009)

Commentationes Mathematicae Universitatis Carolinae

We give a sufficient condition for a curve $γ : ℝ \to ℝ^{n}$ to ensure that the $1$ -dimensional Hausdorff measure restricted to $γ$ is locally monotone.

Local monotonicity of Hausdorff measures restricted to real analytic curves

Robert Černý (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve $γ : ℝ \to ℝ^{N}$ , $N \geq 2$ , is locally 1-monotone.

Lorentzian surfaces in Lorentz three-space are studied using an indefinite version of the quaternions. A classification theorem for Bonnet pairs in Lorentz three-space is obtained.

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Lagrange spaces with indicatrices as constant mean curvature surfaces or minimal surfaces.

Large H-Surfaces Via the Mountain-Pass-Lemma.

Le problème de Dirichlet pour l'équation des surfaces minimales sur des domaines non bornés

Le problème des surfaces à courbure moyenne prescrite

Lignes de divergence pour les graphes à courbure moyenne constante

Linearization and explicit solutions of the minimal surface equations.

Local monotonicity of Hausdorff measures restricted to curves in $ℝ^{n}$

Local monotonicity of Hausdorff measures restricted to real analytic curves

Local monotonicity of measures supported by graphs of convex functions.

Locally isometric families of minimal surfaces.

Lorentzian isothermic surfaces and Bonnet pairs

Currently displaying 1 – 11 of 11