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.
Bernstein and De Giorgi type problems: new results via a geometric approach
We use a Poincaré type formula and level set analysis to detect one-dimensional symmetry of stable solutions of possibly degenerate or singular elliptic equations of the formOur setting is very general and, as particular cases, we obtain new proofs of a conjecture of De Giorgi for phase transitions in and and of the Bernstein problem on the flatness of minimal area graphs in . A one-dimensional symmetry result in the half-space is also obtained as a byproduct of our analysis. Our approach...
Bestimmung einer speciellen Minimalfläche [Book]
Bifurcation of the equivariant minimal interfaces in a hydromechanics problem.
Boundaries of Caccioppoli sets with Hölder-continuois normal vector.
Boundaries of prescribed mean curvature
The existence of a singular curve in is proven, whose curvature can be extended to an function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.
Boundary Configuartions Spanning Contiuna of Minimal Surfaces.
Boundary value problems for non-parametric surfaces of prescribed mean curvature
Branched Immersions of Surfaces and Reduction of Topological Type. II.
Bubbletons in 3-dimensional space forms.
Bubbling on boundary submanifolds for the Lin–Ni–Takagi problem at higher critical exponents
Let be a bounded domain in with smooth boundary . We consider the equation , under zero Neumann boundary conditions, where is open, smooth and bounded and is a small positive parameter. We assume that there is a -dimensional closed, embedded minimal submanifold of , which is non-degenerate, and certain weighted average of sectional curvatures of is positive along . Then we prove the existence of a sequence and a positive solution such that in the sense of measures, where ...
C2-Regularity for Partially Free Minimal Surfaces.