Surfaces of characteristic curvature

Vladimír Fiřt

Displaying similar documents to “Surfaces of characteristic curvature”

Helicoidal surfaces in Minkowski space with constant mean curvature and constant Gauss curvature

Rafael López, Esma Demir (2014)

Open Mathematics

Similarity:

We classify all helicoidal non-degenerate surfaces in Minkowski space with constant mean curvature whose generating curve is a the graph of a polynomial or a Lorentzian circle. In the first case, we prove that the degree of the polynomial is 0 or 1 and that the surface is ruled. If the generating curve is a Lorentzian circle, we prove that the only possibility is that the axis is spacelike and the center of the circle lies on the axis.

On some generalisations of constant mean curvature surfaces.

Fujioka, A., Inoguchi, J. (1999)

Lobachevskii Journal of Mathematics

Similarity:

First variation of the general curvature-dependent surface energy

Günay Doğan, Ricardo H. Nochetto (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise...