A Morse theory for annulus-type minimal surfaces.
A perturbation result concerning a second solution to the Dirichlet problem for the equation of prescribed mean curvature.
A shape-optimization technique for the capillary surface problem.
A Sufflcient Condition for a Critical Point of a Functional to be a Minimum and Its Application to Plateau' s Problem.
An application of eigenfunctions of -Laplacians to domain separation
We are interested in algorithms for constructing surfaces of possibly small measure that separate a given domain into two regions of equal measure. Using the integral formula for the total gradient variation, we show that such separators can be constructed approximatively by means of sign changing eigenfunctions of the -Laplacians, , under homogeneous Neumann boundary conditions. These eigenfunctions turn out to be limits of steepest descent methods applied to suitable norm quotients.
An existence result for minimal spheres in manifolds boundary
We prove the existence of a not homotopically trivial minimal sphere in a 3-manifold with boundary, obtained by deleting an open connected subset from a compact Riemannian oriented 3-manifold with boundary, having trivial second homotopy group.
Area Maximizing Hypersurfaces in Minkowski Space Having an Isolated Singularity.
Bifurcation near solutions of variational problems with degenerate second variation.
Bifurkation von Minimalflächen und elementare Katastrophen.
Coincidence set of minimal surfaces for the thin obstacle.
Complete minimal hypersurfaces with prescribed asymptotics at infinity.
Direct variational methods in nonreflexive spaces
Eine globalanalytische Behandlung des Douglas'schen Problems.
Estimations of the best constant involving the norm in Wente’s inequality and compact -surfaces in euclidean space
Estimations of the best constant involving the L2 norm in Wente's inequality and compact H-surfaces in Euclidean space
In the first part of this paper, we study the best constant involving the L2 norm in Wente's inequality. We prove that this best constant is universal for any Riemannian surface with boundary, or respectively, for any Riemannian surface without boundary. The second part concerns the study of critical points of the associate energy functional, whose Euler equation corresponds to H-surfaces. We will establish the existence of a non-trivial critical point for a plan domain with small holes.
Existence results for embedded minimal surfaces of controlled topological type, III
Harnack’s inequalities for solutions to the mean curvature equation and to the capillarity problem
Hypersurfaces with Constant Mean Curvature and Prescribed Area.
Least area Tori and 3-manifolds of nonnegative scalar curvature.
Maximum principles and minimal surfaces