We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact
forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of this …

Acta Mathematica 2018.221.1.5 Page 1 Acta Math., 221 (2018), 159–202 DOI: 10.4310/ACTA.2018.v221.n1.a5
c 2018 by Institut Mittag-Leffler. All rights reserved Isoperimetric characterization of upper …

We study the intrinsic structure of parametric minimal discs in metric spaces admitting a
quadratic isoperimetric inequality. We associate to each minimal disc a compact, geodesic …

We prove a normal form for contact forms close to a Zoll one and deduce that Zoll contact
forms on any closed manifold are local maximizers of the systolic ratio. Corollaries of this …

We explore a natural generalization of systolic geometry to Finsler metrics and optical
hypersurfaces with special emphasis on its relation to the Mahler conjecture and the …

Our purpose here is to give an overview of known results and open questions concerning
the volume product 𝒫 (K)= minz∈ K vol (K) vol ((K− z)∗) of a convex body K in ℝn. We …

The main subject of this lecture is a connection between Gromov's filling volumes and a
boundary rigidity problem of determining a Riemannian metric in a compact domain by its …

Let $ X $ be a Banach space or more generally a complete metric space admitting a conical
geodesic bicombing. We prove that every closed $ L $-Lipschitz curve $\gamma: S …

We show that the volume of a simple Riemannian metric on D n is locally monotone with
respect to its boundary distance function. Namely if g is a simple metric on D n and g′ is …

We show that every local supremum of the systole over the space of Riemannian metrics of
curvature at most-1 on a given nonsimply connected closed surface is attained by a …