The angle criterion.
The asymptotic behaviour of surfaces with prescribed mean curvature near meeting points of fixed and free boundaries
We study the shape of stationary surfaces with prescribed mean curvature in the Euclidean 3-space near boundary points where Plateau boundaries meet free boundaries. In deriving asymptotic expansions at such points, we generalize known results about minimal surfaces due to G. Dziuk. The main difficulties arise from the fact that, contrary to minimal surfaces, surfaces with prescribed mean curvature do not meet the support manifold perpendicularly along their free boundary, in general.
The cone over the Clifford torus in R4 ist ...-minimizing.
The Cusp Catastrophe of Thom in the Bifurcation of Minimal Surfaces.
The Dirichlet problem for the minimal surface equation with Lipschitz continuous boundary data.
The double bubble problem in spherical and hyperbolic space.
The equivariant Dehn's lemma and loop theorem.
The Existence of Embedded Minimal Surfaces and the Problem of Uniqueness.
The explicit construction of all harmonic two-spheres in G2 (Rn).
The exterior Dirichlet problem for quasi linear elliptic equations with small boundary data.
The exterior plateau problem.
The generalized Favard problem.
The Indes Theorem for k-Fold Connected Minimal Surfaces.
The isoperimetric inequality for a minimal surface with radially connected boundary
The Mumford-Shah conjecture in image processing
The nonexistence of a weak solution of Dirichlet's problem for the functional of minimal surface on nonconvex domains
The obstacle problem for functions of least gradient
For a given domain , we consider the variational problem of minimizing the -norm of the gradient on of a function with prescribed continuous boundary values and satisfying a continuous lower obstacle condition inside . Under the assumption of strictly positive mean curvature of the boundary , we show existence of a continuous solution, with Holder exponent half of that of data and obstacle. This generalizes previous results obtained for the unconstrained and double-obstacle problems. The...
The Obstacle Problem Revisited.
The Plateau-Douglas problem for nonorientable minimal surfaces.
The stable homology of flat torus.