The Indes Theorem for k-Fold Connected Minimal Surfaces.
The isoperimetric inequality for a minimal surface with radially connected boundary
The Kantorovich metric: the initial history and little-known applications.
The Lagrange complex
The lightest plane structures of a bounded stress level transmitting a point load to a circular support
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 mean surface area of the boxes circumscribed about a convex body
The Monge problem for strictly convex norms in
We prove the existence of an optimal transport map for the Monge problem in a convex bounded subset of under the assumptions that the first marginal is absolutely continuous with respect to the Lebesgue measure and that the cost is given by a strictly convex norm. We propose a new approach which does not use disintegration of measures.
The Monge problem on non-compact manifolds
The Mumford-Shah conjecture in image processing
The nonexistence of a weak solution of Dirichlet's problem for the functional of minimal surface on nonconvex domains
The Non-Existence of Branch Points in Solutions to Certain Classes of Plateau Type Variational Problems.
The nonlinear membrane model : a Young measure and varifold formulation
We establish two new formulations of the membrane problem by working in the space of -Young measures and -varifolds. The energy functional related to these formulations is obtained as a limit of the formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing sequences...
The nonlinear membrane model: a Young measure and varifold formulation
We establish two new formulations of the membrane problem by working in the space of -Young measures and -varifolds. The energy functional related to these formulations is obtained as a limit of the 3d formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...
The obstacle problem for functions of least gradient
For a given domain , we consider the variational problem of minimizing the -norm of the gradient on of a function with prescribed continuous boundary values and satisfying a continuous lower obstacle condition inside . Under the assumption of strictly positive mean curvature of the boundary , we show existence of a continuous solution, with Holder exponent half of that of data and obstacle. This generalizes previous results obtained for the unconstrained and double-obstacle problems. The...
The Obstacle Problem Revisited.
The optimal shape of a dendrite sealed at both ends
The parametric Weierstrass integral over a BV curve as a length functional
The constructive definition of the Weierstrass integral through only one limit process over finite sums is often preferable to the more sophisticated definition of the Serrin integral, especially for approximation purposes. By proving that the Weierstrass integral over a BV curve is a length functional with respect to a suitable metric, we discover a further natural reason for studying the Weierstrass integral. This characterization was conjectured by Menger.
The Plateau Problem for Surfaces of Prescribed Mean Curvature in a Cylinder.
The Plateau-Douglas problem for nonorientable minimal surfaces.