arXiv subjects

Averil Aussedat

Publications and source records attributed to Averil Aussedat.

3 recordsLinked to original sources

arXiv2026

Quantified rigidity of $\mathcal{A}$-free Young measure concentrations

We establish quantitative stability of the De Philippis--Rindler rigidity on conical convex regions. By constructing $\mathcal{A}$-quasiconvex functions with a tailored concavity---which additionally yields a new, elementary proof of the original theorem for constant-rank operators---we prove a spreading inequality that strictly limits the angular concentration of $\mathcal{A}$-free measures. This geometric bound establishes that singular concentrations cannot cluster arbitrarily close to a direction outside the Tartar wave cone. As a consequence, we obtain a new $L^1$ compensated compactness result: $\mathcal{A}$-free sequences with uniformly bounded mass are forced to be equi-integrable, thereby preventing the formation of mass concentrations, provided their targets are asymptotically restricted to cones whose aperture is controlled by a power of the distance to the wave cone of $\mathcal A$.

math.AP↗

arXiv2026

Characterization of measures on the real line that are critically unstable under small shifts

We study the perturbation of a measure $\mu \in \mathscr{P}(\mathbb{R})$ consisting in superposing two copies of $\mu$, each slightly shifted by a small distance $\pm h$. The difference between $\mu$ and its perturbation is measured with a Wasserstein distance. For any $\mu$, this distance is bounded from above by $h$. We show that measures for which this critical rate is achieved when $h$ goes to 0 are characterized as the ones giving most of their mass to some particular porous sets. This is used to identify which measures $\mu$ on the real line have a 2-Wasserstein tangent cone equal to the set of directions inducing curves with maximal initial speed.

math.OC↗

arXiv2025

Locality of centred tangent cones in the Wasserstein space

The geometric tangent cone to a probability measure $\mu$ is a set of measure-valued applications that are almost geodesics. This is a nonlocal condition, typically lost when conditioning the measure on a given set. We show that if one removes the barycenter of any element of the tangent cone, then the resulting set of centred measure fields is characterized by a local condition. Precisely, centred tangent fields must be concentrated on a family of vector subspaces attached to any point, and these subspaces correspond to the normal spaces to some sets of ``dimension $k$'' on which the measure $\mu$ is concentrated.

math.MG↗