Stability of Hypersurfaces with Constant Mean Curvature.
Structural optimization using topological and shape sensitivity via a level set method
Sufficient Conditions for a Pair of n-Planes to be Area-Minimizing.
Surfaces quasiminimales de codimension 1 et domaines de John
Surfaces quasiminimales de codimension 1 : un morceau de démonstration
Tangency properties of sets with finite geometric curvature energies
We investigate tangential regularity properties of sets of fractal dimension, whose inverse thickness or integral Menger curvature energies are bounded. For the most prominent of these energies, the integral Menger curvature , where κ(x,y,z) is the inverse circumradius of the triangle defined by x,y and z, we find that for p ≥ 3α implies the existence of a weak approximate α-tangent at every point of the set, if some mild density properties hold. This includes the scale invariant case p = 3 for...
The angle criterion.
The BV-energy of maps into a manifold : relaxation and density results
Let be a smooth compact oriented riemannian manifoldwithout boundary, and assume that its -homology group has notorsion. Weak limits of graphs of smooth maps with equibounded total variation give riseto equivalence classes of cartesian currents in for which we introduce a natural-energy.Assume moreover that the first homotopy group of iscommutative. In any dimension we prove that every element in can be approximatedweakly in the sense of currents by a sequence of graphs...
The Cauchy stress theorem for bodies with finite perimeter
The complete figure for second order multiple integral problems in the calculus of variations. (Short Communication).
The complete figure for second order multiple integral problems in the calculus of variations.
The control problem : A comment on an article by J. Kučera
The control problem
The Curvature of a Set with Finite Area
In a paper, by myself, E. Gonzalez and I. Tamanini (see [2]), it was proven that all sets of finite perimeter do have a non trivial variational property, connected with the mean curvature of their boundaries. In the present article, that variational property is made more precise.
The Hessian of the distance from a surface in the Heisenberg group.
The mean curvature of a Lipschitz continuous manifold
The paper is devoted to the description of some connections between the mean curvature in a distributional sense and the mean curvature in a variational sense for several classes of non-smooth sets. We prove the existence of the mean curvature measure of by using a technique introduced in [4] and based on the concept of variational mean curvature. More precisely we prove that, under suitable assumptions, the mean curvature measure of is the weak limit (in the sense of distributions) of the mean...
The Singular Set of an energy minimzing map from B4 to S2.
The Weierstrass integral in the complex plane
Trace inequalities for Carnot-Carathéodory spaces and applications
Transport problems and disintegration maps
By disintegration of transport plans it is introduced the notion of transport class. This allows to consider the Monge problem as a particular case of the Kantorovich transport problem, once a transport class is fixed. The transport problem constrained to a fixed transport class is equivalent to an abstract Monge problem over a Wasserstein space of probability measures. Concerning solvability of this kind of constrained problems, it turns out that in some sense the Monge problem corresponds to a...