Related papers: Young measures, Cartesian maps, and polyconvexity

This work is devoted to the study of two-scale gradient Young measures naturally arising in nonlinear elasticity homogenization problems. Precisely, a characterization of this class of measures is derived and an integral representation…

We show that there are minimal graphs in R^{n+1} whose intersection with the portion of the horizontal hyperplane contained in the unit ball has any prescribed geometry, up to a small deformation. The proof hinges on the construction of…

Necessary and sufficient conditions are given for the Palais-Smale Condition C to hold for the Yang-Mills functional for connections that are invariant under a Lie group action on the manifold with orbits of codimension less than or equal…

We compare existence and equivariance phenomena for weak moment maps and homotopy moment maps in multisymplectic geometry.

This work presents a general principle, in the spirit of convex integration, leading to a method for the characterization of Young measures generated by gradients of maps in $W^{1,p}$ with $p$ less than the space dimension, whose Jacobian…

Let M_n stand for the Plancherel measure on Y_n, the set of Young diagrams with n boxes. A recent result of Stanley (arXiv:0807.0383) says that for certain functions G defined on the set Y of all Young diagrams, the average of G with…

Methods of hypotheses testing for equality of extrinsic antimeans on compact manifolds are unveiled in this paper. The two and multiple sample problem for antimeans on compact manifolds is addressed for large samples via asymptotic…

Fold maps are higher dimensional versions of Morse functions, which play important roles in the studies of smooth manifolds, and such general maps also have been fundamental tools in the studies of smooth manifolds by using generic maps. In…

In this paper, we study multiplicity of solutions of the Yamabe problem on product manifolds with minimal boundary via bifurcation theory.

The marginal maximum a posteriori probability (MAP) estimation problem, which calculates the mode of the marginal posterior distribution of a subset of variables with the remaining variables marginalized, is an important inference problem…

Let $\mathcal{M}$ be a compact manifold of $\mathbb{R}^d$. The goal of this paper is to decide, based on a sample of points, whether the interior of $\mathcal{M}$ is empty or not. We divide this work in two main parts. Firstly, under a…

We prove tight upper bounds for the number of vertices of a simple polygon that is the union or the intersection of two simple polygons with given numbers of convex and concave vertices. The similar question on graphs of the lower (or…

Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…

We use multiplication maps to give a characteristic-free approach to vanishing theorems on toric varieties. Our approach is very elementary but is enough powerful to prove vanishing theorems.

Let $X$ be an irreducible algebraic variety over $\mathbb{C}$, endowed with an algebraic foliation ${\cal{F}}$. In this paper, we introduce the notion of minimal invariant variety $V({\cal{F}},Y)$ with respect to $({\cal{F}},Y)$, where $Y$…

We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer…

Let $M$ be a fixed compact oriented embedded submanifold of a manifold $\overline{M}$. Consider the volume $\mathcal{V} (\overline{g}) = \int_M \mathsf{vol}_{(M, g)}$ as a functional of the ambient metric $\overline{g}$ on $\overline{M}$,…

We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…

We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones;…

We adapt the concept of $\mathcal{K}-$convergence of Young measures to the sequences of approximate solutions resulting from numerical schemes. We obtain new results on pointwise convergence of numerical solutions in the case when solutions…