C2-Regularity for Partially Free Minimal Surfaces.
Capillary Surfaces in Negative Gravitational Fields.
Coincidence set of minimal surfaces for the thin obstacle.
Comparison principles and Liouville theorems for prescribed mean curvature equations in unbounded domains
Complete minimal hypersurfaces in hyperbolic n-manifolds.
Complete minimal hypersurfaces with prescribed asymptotics at infinity.
Complete Non-Orientable Minimal Surfaces in ℝ 3 and Asymptotic Behavior
In this paperwe give new existence results for complete non-orientable minimal surfaces in ℝ3 with prescribed topology and asymptotic behavior
Complete nonorientable minmal surfaces in R3.
Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
There is an obvious topological obstruction for a finite energy unimodular harmonic extension of a -valued function defined on the boundary of a bounded regular domain of . When such extensions do not exist, we use the Ginzburg-Landau relaxation procedure. We prove that, up to a subsequence, a sequence of Ginzburg-Landau minimizers, as the coupling parameter tends to infinity, converges to a unimodular harmonic map away from a codimension-2 minimal current minimizing the area within the homology...
Conformal mappings and the Plateau-Douglas problem in Riemannian manifolds.
Continuity of Minimal Surfaces with Piecewise Smooth Free Boundaries.
Convex Hull Property and Exclosure Theorems for H-Minimal Hypersurfaces in Carnot Groups
In this paper, we generalize to sub-Riemannian Carnot groups some classical results in the theory of minimal submanifolds. Our main results are for step 2 Carnot groups. In this case, we will prove the convex hull property and some “exclosure theorems” for H-minimal hypersurfaces of class C2 satisfying a Hörmander-type condition.
Cross ratios, Anosov representations and the energy functional on Teichmüller space
We study two classes of linear representations of a surface group: Hitchin and maximal symplectic representations. We relate them to cross ratios and thus deduce that they are displacing which means that their translation lengths are roughly controlled by the translations lengths on the Cayley graph. As a consequence, we show that the mapping class group acts properly on the space of representations and that the energy functional associated to such a representation is proper. This implies the existence...
Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals.
Curvature estimates for minimal hypersurfaces in singular spaces.
Curvature estimates for minimal surfaces in -manifolds
Curvature functionals for curves in the equi-affine plane
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.