Related papers: Young measures, Cartesian maps, and polyconvexity
In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…
Young's integral inequality is reformulated with upper and lower bounds for the remainder. The new inequalities improve Young's integral inequality on all time scales, such that the case where equality holds becomes particularly transparent…
We give new upper bounds for the number of nonconstant holomorphic maps depending only on the genus. Our estimates improve previously known bounds. The proof is based on the study of pullbacks of holomorphic differentials, together with…
An O(n) test for polygon convexity is stated and proved. It is also proved that the test is minimal in a certain exact sense.
Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…
We demonstrate the existence of quasiconformal mappings on closed manifolds that cannot be decomposed as a composition of mappings with arbitrarily small conformal distortion.
We establish the existence and symmetry of all minimizers of a constrained variational problem involving the fractional gradient. This problem is closely connected to some fractional kinetic equations.
When the plane is pie-sliced in $n\leq 4$ parts (with nonempty interior and common vertex at the origin) our main result provides a sufficient condition for any map $L$, that is continuous and piecewise linear relatively to this slicing, to…
We prove general mixing theorems for sequences of meromorphic maps on compact K\"ahler manifolds. We deduce that the bifurcation measure is exponentially mixing for a family of rational maps of $\mathbb{P}^q(\mathbb{C})$ endowed with…
We compute the minimum number of critical points of a small codimension smooth map between two manifolds. We give as well some partial results for the case of higher codimension when the manifolds are spheres.
We show that for a large class of maps on manifolds of arbitrary finite dimension, the existence of a Gibbs-Markov-Young structure (with Lebesgue as the reference measure) is a necessary as well as sufficient condition for the existence of…
We introduce a class of variational principles on measure spaces which are causal in the sense that they generate a relation on pairs of points, giving rise to a distinction between spacelike and timelike separation. General existence…
In this paper, we give a uniqueness theorem for the Dirichlet problem of minimal maps into general Riemannian manifolds with non-positive sectional curvature, improving Theorem 5.2 of Lee-Ooi-Tsui's paper published in J. Geom. Anal.. The…
We investigate the approximation of Monge--Kantorovich problems on general compact metric spaces, showing that optimal values, plans and maps can be effectively approximated via a fully discrete method. First we approximate optimal values…
We consider the inverse problem of estimating an unknown function $u$ from noisy measurements $y$ of a known, possibly nonlinear, map $\mathcal{G}$ applied to $u$. We adopt a Bayesian approach to the problem and work in a setting where the…
In this paper, we present a novel approach for analyzing the relationship between the supports of conditional measures and their geometric arrangement in Wasserstein space via the disintegration map. Our method establishes criteria to…
In this note, we derive a uniqueness theorem for minimal graphs of general codimension under certain restrictions closed related to the convexity (not strict convexity) of the area functional with respect to singular values, improving the…
We establish general assumptions under which a constrained vari- ational problem involving the fractional gradient and a local nonlin- earity admits minimizers.
We characterize generalized Young measures, the so-called DiPerna-Majda measures which are generated by sequences of gradients. In particular, we precisely describe these measures at the boundary of the domain in the case of the…
On an abstract Wiener space, assume that T is the solution of the quadratic Monge problem associated to the Wiener measure and a second one with a Radon-Nikodym derivative of exponential type. Under the finite information hypothesis, using…