Existence, Regularity, and Boundary Behaviour of Generalized Surfaces of Prescribed Mean Curvature.
Existence results for embedded minimal surfaces of controlled topological type, II
Existence results for embedded minimal surfaces of controlled topological type, I
Existence results for embedded minimal surfaces of controlled topological type, III
Extending Minimal Varieties.
First variation of the general curvature-dependent surface energy
We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise derivation...
First variation of the general curvature-dependent surface energy
We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the mean curvature of the surface. Energies of this form have applications in many areas, such as materials science, biology and image processing. Often one is interested in finding a surface that minimizes such an energy, which entails finding its first variation with respect to perturbations of the surface. We present a concise derivation...
Flächen beschränkter mittlerer Krümmung in einer dreidimensionalen Riemannschen Mannigfaltigkeit.
Flächen vorgeschriebener mittlerer Krümmung mit eindeutiger Projektion auf eine Ebene.
Geometric Properties of Minimal Surfaces with Free Boundaries.
Global regularity for solutions of the minimal surface equation with continuous boundary values
Gradient estimates and Harnack inequalities for solutions to the minimal surface equation
A gradient estimate for solutions to the minimal surface equation can be proved by Partial Differential Equations methods, as in [2]. In such a case, the oscillation of the solution controls its gradient. In the article presented here, the estimate is derived from the Harnack type inequality established in [1]. In our case, the gradient is controlled by the area of the graph of the solution or by the integral of it. These new results are similar to the one announced by Ennio De Giorgi in [3].
Gradient theory of phase transitions with boundary contact energy
Gyroids of constant mean curvature.
Hölder regularity of three-dimensional minimal cones in ℝⁿ
We show the local Hölder regularity of Almgren minimal cones of dimension 3 in ℝⁿ away from their centers. The proof is almost elementary but we use the generalized theorem of Reifenberg. In the proof, we give a classification of points away from the center of a minimal cone of dimension 3 in ℝⁿ, into types ℙ, 𝕐 and 𝕋. We then treat each case separately and give a local Hölder parameterization of the cone.
How to blow infinitely large soap bubbles with a fixed boundary
Il problema della capillarità su domini non regolari
Il problema di Plateau in domini illimitati
Infinite boundary value problems for surfaces of prescribed mean curvature
Infinite periodic discrete minimal surfaces without self-intersections.