An integral formula for Willmore surfaces in an -dimensional sphere.
An optimal estimate of the free boundary of a minima surface.
An unknotting result for complete minimal surfaces R3.
Applications of Quaternionic Holomorphic Geometry to minimal surfaces
In this paper we give a survey of methods of Quaternionic Holomorphic Geometry and of applications of the theory to minimal surfaces. We discuss recent developments in minimal surface theory using integrable systems. In particular, we give the Lopez–Ros deformation and the simple factor dressing in terms of the Gauss map and the Hopf differential of the minimal surface. We illustrate the results for well–known examples of minimal surfaces, namely the Riemann minimal surfaces and the Costa surface....
Apriori estimates of the principal curvatures for immersions of prescribed mean curvature and theorems of Bernstein-type.
Area minimizing hypersurfaces with isolated singularities.
Asymmetric unbounded liquid bridges
Asymptotic behaviour of minimal graphs over exterior domains
Asymptotic values of minimal graphs in a disc
We consider solutions of the prescribed mean curvature equation in the open unit disc of euclidean n-dimensional space. We prove that such a solution has radial limits almost everywhere; which may be infinite. We give an example of a solution to the minimal surface equation that has finite radial limits on a set of measure zero, in dimension two. This answers a question of Nitsche.