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In this paper, we investigate properties of entropy-penalized Wasserstein barycenters introduced by Bigot, Cazelles and Papadakis (2019) as a regularization of Wasserstein barycenters first presented by Agueh and Carlier (2011). After…

We present the Laplace operator associated to a hyperbolic surface $\Gamma\setminus\mathbb{H}$ and a unitary representation of the fundamental group $\Gamma$, extending the previous definition for hyperbolic surfaces of finite area to those…

The purpose of this article is to present a result on the existence of Cauchy temporal functions invariant by the action of a compact group of conformal transformations in arbitrary globally hyperbolic manifolds. Moreover, the previous…

We show that the ergodic, topological and geometric basins coincide for hyperbolic dominated ergodic $cu$-Gibbs states, solving the ``basin problem'' for a wide class of non-uniformly hyperbolic systems. We obtain robust examples of…

We study the dynamics of unipotent flows on frame bundles of hyperbolic manifolds of infinite volume. We prove that they are topologi-cally transitive, and that the natural invariant measure, the so-called " Burger-Roblin measure ", is…

We outline a toy model in which a unique mechanism may trigger a dynamical chain resulting in key low-energy regularities. The starting points are a negative cosmological term in the bulk and conformally invariant nongravity sector. These…

Here we study the space of real hyperbolic plane curves that are invariant under actions of the cyclic and dihedral groups and show they have determinantal representations that certify this invariance. We show an analogue of Nuij's theorem…

By use of H. C. Wang's bound on the radius of a ball embedded in the fundamental domain of a lattice of a semisimple Lie group, we construct an explicit lower bound for the volume of a quaternionic hyperbolic orbifold that depends only on…

In a previous work, P. Briand and Y. Hu proved the uniqueness among the solutions which admit every exponential moments. In this paper, we prove that uniqueness holds among solutions which admit some given exponential moments. These…

For every hyperplane $H$ supporting a convex body $C$ in the hyperbolic space $\mathbb{H}^d$ we define the width of $C$ determined by $H$ as the distance between $H$ and a most distant ultraparallel hyperplane supporting $C$. We prove that…

In the Wigner-covariant rest-frame instant form of dynamics it is possible to develop a relativistic kinematics for the N-body problem. The Wigner hyperplanes define the intrinsic rest frame and realize the separation of the center-of-mass.…

Let $D$ be a bounded domain in a complex Banach space. According to the Earle-Hamilton fixed point theorem, if a holomorphic mapping $F : D \mapsto D$ maps $D$ strictly into itself, then it has a unique fixed point and its iterates converge…

Pogorelov's rigidity theorem states that a compact convex body in the hyperbolic 3-space is determined up to isometry by the intrinsic path metric on its boundary. The main result of this paper addresses a rigidity problem for non-compact…

We construct geometrically infinite hyperbolic surfaces supporting horocycles with tailored recurrence properties. In particular, we obtain the first examples of non-trivial minimal horocyclic orbit closures and of infinite locally-finite…

We give a short and simple proof of a recent result of Dobbins that any point in an $nd$-polytope is the barycenter of $n$ points in the $d$-skeleton. This new proof builds on the constraint method that we recently introduced to prove…

We characterize the extreme and exposed points of the unit ball (with respect to the $L^1$-norm) in the shift-invariant space generated by the Gaussian function, as well as in the quasi shift-invariant space generated by the hyperbolic…

For the classical $N$-body problem in $\mathbb{R}^d$ with $d\ge2$, Maderna-Venturelli in their remarkable paper [Ann. Math. 2020] proved the existence of hyperbolic motions with any positive energy constant, starting from any configuration…

For a hypersurface V of a conformal space, we introduce a conformal differential invariant I = h^2/g, where g and h are the first and the second fundamental forms of V connected by the apolarity condition. This invariant is called the…

The paper consists of two parts. In the first one we show that a relatively hyperbolic group $G$ splits as a star graph of groups whose central vertex group is finitely generated and the other vertex groups are maximal parabolic subgroups.…

Let $X$ be a building, identified with its Davis realisation. In this paper, we provide for each $x\in X$ and each $\eta$ in the visual boundary $\partial X$ of $X$ a description of the geodesic ray bundle $Geo(x,\eta)$, namely, of the…