Let $M$ be a compact connected manifold of dimension $n$ endowed with a conformal class $C$ of Riemannian metrics of volume one. For any integer $k\geq0$, we consider the conformal invariant $\lambda_k ^c (C)$ defined as the supremum of the $k$-th eigenvalue $\lambda_k (g)$ of the Laplace-Beltrami operator $\Delta_g$, where $g$ runs over $C$. First...
This paper deals with the geometry of metric "two dimensional" spaces, equipped with semi-flows admitting transverse foliations by forests. Our main theorem relates the Gromov-hyperbolicity of such spaces, for instance mapping-telescopes of trees, with the dynamical behaviour of the semi-flow. As a corollary, we give a new proof of Bestvina-Feighn ...
In this work we study the Hausdorff dimension of measures whose weight distribution satisfies a markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the Tricot dimensions (packing dimension) equal the upper Rényi ...
An index evaluating the amount of chirality of a mixture of colored random variables is defined. Properties are established. Extreme chiral mixtures are characterized and examples are given. Connections between chirality, Wasserstein distances, and least squares Procrustes methods are pointed out.
Le séminaire "Histoires de Géométries", mis en place à la FMSH par l'équipe F2DS dirigée par Dominique FLAMENT (directeur de recherche, CNRS), se veut largement ouvert. Non seulement il est un lieu de rencontre d'excellence entre mathématiciens, philosophes et historiens des sciences, mais il s'ouvre également à un public de "curieux", plus dispers...
This paper is devoted to the study of critical metrics of the trace of the heat kernel on a compact manifold. We obtain various characterizations of such metrics and investigate their geometric properties. We also give a complete classification of critical metrics on surfaces of genus zero and one.
International audience
International audience
Cet article contient des remarques sur les polygones croisés et le partage du plan par une droite. Après une introduction sur les parallélogrammes en cinquième et un rappel concernant des propriétés de convexité des demi-plans, il propose deux activités géométriques. La première met en jeu les pieds des bissectrices d'un triangle. La seconde propos...
The properties of the root mean square chiral index of a d-dimensional set of n points, previously investigated for planar sets, are examined for spatial sets. The properties of the root mean squares direct symmetry index, defined as the normalized minimized sum of the n squared distances between the vertices of the d-set and the permuted d-set, ar...
