18 citations · 92 across the 40 of their papers we have counts for
44 papers
On the concave one-dimensional random assignment problem and Young integration theory
Michael Goldman, Dario Trevisan
We investigate the one-dimensional random assignment problem in the concave case, i.e., the assignment cost is a concave power function, with exponent , of the distance betw…
From energy bounds to dimensional estimates in a branched transport model for type-I superconductors
Guido De Philippis, Michael Goldman, Berardo Ruffini
We consider a branched transport type problem which describes the magnetic flux through type-I superconductors in a regime of very weak applied fields. At the boundary of the sampl…
A deformation theorem for tensor flat chains and applications (complement to ''Tensor rectifiable G-flat chains'')
Michael Goldman, Benoît Merlet
In this note we extend White's deformation theorem for G-flat chains to the setting of G-flat tensor chains. As a corollary we obtain that the groups of normal tensor chains identi…
Tensor rectifiable G-flat chains
Michael Goldman, Benoît Merlet
A rigidity result for normal rectifiable -chains in with coefficients in an Abelian normed group is established. Given some decompositions , $n=n_1+n_2…
Set-decomposition of normal rectifiable G-chains via an abstract decomposition principle
Michael Goldman, Benoît Merlet
We introduce the notion of set-decomposition of a normal G-flat chain. We show that any normal rectifiable -flat chain admits a decomposition in set-indecomposable sub-chains. T…
Optimal transport methods for combinatorial optimization over two random point sets
Michael Goldman, Dario Trevisan
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in where the edge cost between two poin…
Uniform -regularity for almost-minimizers of some nonlocal perturbations of the perimeter
Michael Goldman, Benoît Merlet, Marc Pegon
In this paper, we establish a -regularity theorem for almost-minimizers of the functional , where and $P_{\vare…
Rigidity of the ball for an isoperimetric problem with strong capacitary repulsion
Michael Goldman, Matteo Novaga, Berardo Ruffini
We consider a variational problem involving competition between surface tension and charge repulsion. We show that, as opposed to the case of weak (short-range) interactions where…
Compactness and structure of zero-states for unoriented Aviles-Giga functionals
Michael Goldman, Benoit Merlet, Marc Pegon +1
Motivated by some models of pattern formation involving an unoriented director field in the plane, we study a family of unoriented counterparts to the Aviles-Giga functional. We in…
On the quadratic random matching problem in two-dimensional domains
Luigi Ambrosio, Michael Goldman, Dario Trevisan
We investigate the average minimum cost of a bipartite matching, with respect to the squared Euclidean distance, between two samples of n i.i.d. random points on a bounded Lipschit…
Existence and stability results for an isoperimetric problem with a non-local interaction of Wasserstein type
Jules Candau-Tilh, Michael Goldman
The aim of this paper is to prove the existence of minimizers for a variational problem involving the minimization under volume constraint of the sum of the perimeter and a non-loc…
A fluctuation result for the displacement in the optimal matching problem
Michael Goldman, Martin Huesmann
The aim of this paper is to justify in dimensions two and three the ansatz of Caracciolo et al. stating that the displacement in the optimal matching problem is essentially given b…
Reifenberg flatness for almost-minimizers of the perimeter under minimal assumptions
Michael Goldman, Matteo Novaga, Berardo Ruffini
The aim of this note is to prove that almost-minimizers of the perimeter are Reifenberg flat, for a very weak notion of minimality. The main observation is that smallness of the ex…
Convergence of asymptotic costs for random Euclidean matching problems
Michael Goldman, Dario Trevisan
We investigate the average minimum cost of a bipartite matching between two samples of n independent random points uniformly distributed on a unit cube in d 3 dimensions, whe…
An --regularity result for optimal transport maps between continuous densities
Michael Goldman
The aim of this short note is to extend the recent variational proof of partial regularity for optimal transport maps to the case of continuous densities.
A variational approach to regularity theory in optimal transportation
Michael Goldman
This paper describes recent results obtained in collaboration with M. Huesmann and F. Otto on the regularity of optimal transport maps. The main result is a quantitative version of…
Non-convex functionals penalizing simultaneous oscillations along independent directions: rigidity estimates
Michael Goldman, B. Merlet
We study a family of non-convex functionals on the space of measurable functions. T…
Quantitative linearization results for the Monge-Ampère equation
Michael Goldman, Martin Huesmann, Felix Otto
This paper is about quantitative linearization results for the Monge-Ampère equation with rough data. We develop a large-scale regularity theory and prove that if a measure is…
A two-point function approach to connectedness of drops in convex potentials
Michael Goldman, Guido De Philippis
We establish connectedness of volume constrained minimisers of energies involving surface tensions and convex potentials. By a previous result of McCann, this implies that minimise…
A large-scale regularity theory for the Monge-Ampere equation with rough data and application to the optimal matching problem
Michael Goldman, Martin Huesmann, Felix Otto
The aim of this paper is to obtain quantitative bounds for solutions to the optimal matching problem in dimension two. These bounds show that up to a logarithmically divergent shif…
A gradient flow approach to relaxation rates for the multi-dimensional Cahn-Hilliard equation
Michael Goldman, Lucia De Luca, Marta Strani
The aim of this paper is to study relaxation rates for the Cahn-Hilliard equation in dimension larger than one. We follow the approach of Otto and Westdickenberg based on the gradi…
Quantitative estimates for bending energies and applications to non-local variational problems
Michael Goldman, Matteo Novaga, Matthias Röger
We discuss a variational model, given by a weighted sum of perimeter, bending and Riesz interaction energies, that could be considered as a toy model for charged elastic drops. The…
A Ginzburg-Landau model with topologically induced free discontinuities
Michael Goldman, Benoît Merlet, Vincent Millot
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed…
Equilibrium shapes of charged droplets and related problems: (mostly) a review
Michael Goldman, Berardo Ruffini
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either rest…