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.