Minimal Varieties and Harmonic Maps in Tori.
Minimalflächen mit freiem Rand in Riemannschen Mannigfaltigkeiten.
Minimalflächen mit polygonalem Rand.
Minimizing the squared mean curvature integral for surfaces in space forms.
Minkowski minimal surfaces in with minimal focal surfaces.
Multiple convex hypersurfaces with prescribed mean curvature
Multiple surfaces of non-constant mean curvature.
Natural algebraic representation formulas for curves in ℂ³
We consider several explicit examples of solutions of the differential equation Φ₁’²(z) + Φ₂’²(z) + Φ₃’²(z) = d²(z) of meromorphic curves in ℂ³ with preset infinitesimal arclength function d(z) by nonlinear differential operators of the form (f,h,d) → V(f,h,d), V = (Φ₁,Φ₂,Φ₃), whose arguments are triples consisting of a meromorphic function f, a meromorphic vector field h, and a meromorphic differential 1-form d on an open set U ⊂ ℂ or, more general, on a Riemann surface Σ. Most of them are natural...
Neue Erzeugungen der Minmalflächen von G. Thomsen.
New characterizations of linear Weingarten hypersurfaces immersed in the hyperbolic space
In this paper, we deal with complete linear Weingarten hypersurfaces immersed in the hyperbolic space , that is, complete hypersurfaces of whose mean curvature and normalized scalar curvature satisfy for some , . In this setting, under appropriate restrictions on the mean curvature and on the norm of the traceless part of the second fundamental form, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of . Furthermore, a rigidity result...
New constant mean curvature surfaces.
New results on the classical problem of Plateau on the existence of many solutions
New stability results for spheres and Wulff shapes
We prove that a closed convex hypersurface of the Euclidean space with almost constant anisotropic first and second mean curvatures in the -sense is -close (up to rescaling and translations) to the Wulff shape. We also obtain characterizations of geodesic hyperspheres of space forms improving those of [Ro1] and [Ro].
New surfaces of constant mean curvature.
Non Existence and Existence of Capillary Surfaces.
Non uniqueness and uniqueness of capillary surfaces.
Note sur l'impossibilité de la quadrature du cercle
Notiz über die algebraischen Minimumsflächen
Numerical finiteness results for minimal surfaces in three-dimensional space forms.
Numerical solution of soap film dual problems.