Isoperimetric Inequalities and the Problem of Plateau.
...k-rectifiable sets.
Lagrangian formalism in the classical field theory
Least-volume representatives of homology classes in
Limiti di problemi di Dirichlet nonlineari in domini variabili
Si studia il comportamento limite di successioni di problemi variazionali nonlineari con condizioni al contorno di Dirichlet su aperti variabili. I principali strumenti usati in questa ricerca sono le nozioni di -convergenza e di -capacità nonlineare.
Local monotonicity of Hausdorff measures restricted to curves in
We give a sufficient condition for a curve to ensure that the -dimensional Hausdorff measure restricted to is locally monotone.
Local monotonicity of Hausdorff measures restricted to real analytic curves
We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve , , is locally 1-monotone.
Local monotonicity of measures supported by graphs of convex functions.
Measurability of classes of Lipschitz manifolds with respect to Borel -algebra of Vietoris topology
Metric currents and geometry of Wasserstein spaces
Metric space valued functions of bounded variation
Minimal hypersurfaces asymptotic to quadratic cones in Zn + 1.
Minimal rearrangements of Sobolev functions : a new proof
Minimizing movements for dislocation dynamics with a mean curvature term
We prove existence of minimizing movements for the dislocation dynamics evolution law of a propagating front, in which the normal velocity of the front is the sum of a non-local term and a mean curvature term. We prove that any such minimizing movement is a weak solution of this evolution law, in a sense related to viscosity solutions of the corresponding level-set equation. We also prove the consistency of this approach, by showing that any minimizing movement coincides with the smooth evolution...
Note on coarea formulae in the Heisenberg group.
We show a first nontrivial example of coarea formula for vector-valued Lipschitz maps defined on the three dimensional Heisenberg group. In this coarea formula, integration on level sets is performed with respect to the 2-dimensional spherical Hausdorff measure, built by the Carnot-Carathéodory distance. The standard jacobian is replaced by the so called horizontal jacobian, corresponding to the jacobian of the Pansu differential of the Lipschitz map. Joining previous results, we achieve all possible...
Note sur l'impossibilité de la quadrature du cercle
On a general coarea inequality and applications.
On a variational property of integral functionals and related conjectures
The aim of this paper is to give the proofs of those results that in [4] were only announced, and, at the same time, to propose some possible developments, indicating some of the most significant open problems.
On a variational theory of image amodal completion
On Conditions for Unrectifiability of a Metric Space
We find necessary and sufficient conditions for a Lipschitz map f : E ⊂ ℝk → X into a metric space to satisfy ℋk(f(E)) = 0. An interesting feature of our approach is that despite the fact that we are dealing with arbitrary metric spaces, we employ a variant of the classical implicit function theorem. Applications include pure unrectifiability of the Heisenberg groups.