On seven points in the boundary of a plane convex body in large relative distances.
On star duality of mixed intersection bodies.
On the Busemann-Petty Problem for Perturbations of the Ball.
On the Exact Constant in the Quantitative Steinitz Theorem in the Plane.
On the isotropic constant of marginals
We show that if μ₁, ..., μₘ are log-concave subgaussian or supergaussian probability measures in , i ≤ m, then for every F in the Grassmannian , where N = n₁ + ⋯ + nₘ and n< N, the isotropic constant of the marginal of the product of these measures, , is bounded. This extends known results on bounds of the isotropic constant to a larger class of measures.
On the monotonicity of the volume of hyperbolic convex polyhedra.
On the stability of the unit circle with minimal self-perimeter in normed planes
We prove a stability result on the minimal self-perimeter L(B) of the unit disk B of a normed plane: if L(B) = 6 + ε for a sufficiently small ε, then there exists an affinely regular hexagon S such that S ⊂ B ⊂ (1 + 6∛ε) S.
On the volume of a certain polytope.
On the volume of the double stochastic matrices.
One functional-analytical idea by Alexandrov in convex geometry.
Optimizing geometric measures for fixed minimal annulus and inradius.
Orthant spanning simplexes with minimal volume.
Profil isopérimétrique, métriques périodiques et formes d'équilibre des cristaux
On donne un développement asymptotique du profil iso pé ri mé tri que de muni d'une métrique riemannienne périodique, et des conséquences pour le problème de la forme d'équilibre des cristaux.
Relative isodiametric inequalities.
Sobolev and isoperimetric inequalities for degenerate metrics.
Solution branching of a general perimeter partition problem.
Some inequalities between two polygons inscribed one in the other.
Some Inequalities for Planar Convex Figures.
Some inequalities for the -curvature image.
Stabilité isopérimétrique