Convergence de variétés et convergence du spectre du laplacien
Convergence of Riemannian manifolds and Laplace operators. I
We study the spectral convergence of compact Riemannian manifolds in relation with the Gromov-Hausdorff distance and discuss the geodesic distances and the energy forms of the limit spaces.
Counterexample to the convexity of level sets of solutions to the mean curvature equation
The convexity of level sets of solutions to the mean curvature equation is a long standing open problem. In this paper we give a counterexample to it.
Courbure des sommes de métriques
Cubical 2-complexes with the 8-property admit a strongly convex metric.
Curvature contents of geometric spaces.
Curvature testing in 3-dimensional metric polyhedral complexes.
Curvature-decreasing maps are volume-decreasing. On joint work with G. Besson and G. Courtois.
De Lellis-Topping type inequalities for f-Laplacians
We establish an integral geometric inequality on a closed Riemannian manifold with ∞-Bakry-Émery Ricci curvature bounded from below. We also obtain similar inequalities for Riemannian manifolds with totally geodesic boundary. In particular, our results generalize those of Wu (2014) for the ∞-Bakry-Émery Ricci curvature.
Deformations of asymptotically cylindrical coassociative submanifolds with fixed boundary.
Deformations of Some ...-Structures.
Deformations of structures, embedding of a Riemannian manifold in a Kählerian one and geometric antigravitation
Tubular neighborhoods play an important role in modern differential topology. The main aim of the paper is to apply these constructions to geometry of structures on Riemannian manifolds. Deformations of tensor structures on a normal tubular neighborhood of a submanifold in a Riemannian manifold are considered in section 1. In section 2, this approach is used to obtain a Kählerian structure on the corresponding normal tubular neighborhood of the null section in the tangent bundle TM of a smooth manifold...
Demostración de Hamilton-Perelman de las conjeturas de Poincaré y Thurston.
Differentiable sphere theorems for Ricci curvature.
Differential geometric structures of stable state feedback systems with dual connections
Dilations associated to flat curves.
I would like to give an exposition of the recent work of Tony Carbery, Mike Christ, Jim Vance, David Watson and myself concerning Hilbert transforms and Maximal functions along curves in R2 [CCVWW].
Dirac and Plateau billiards in domains with corners
Groping our way toward a theory of singular spaces with positive scalar curvatures we look at the Dirac operator and a generalized Plateau problem in Riemannian manifolds with corners. Using these, we prove that the set of C 2-smooth Riemannian metrics g on a smooth manifold X, such that scalg(x) ≥ κ(x), is closed under C 0-limits of Riemannian metrics for all continuous functions κ on X. Apart from that our progress is limited but we formulate many conjectures. All along, we emphasize geometry,...
Discrétisation de zeta-déterminants d’opérateurs de Schrödinger sur le tore
Nous donnons ici deux résultats sur le déterminant -régularisé d’un opérateur de Schrödinger sur une variété compacte . Nous construisons, pour , une suite où est un graphe fini qui se plonge dans via de telle manière que soit une triangulation de et où est un laplacien discret sur tel que pour tout potentiel sur , la suite de réels converge après renormalisation vers . Enfin, nous donnons sur toute variété riemannienne compacte de dimension inférieure ou égale à ...
Dubins' problem is intrinsically three-dimensional
Dubins' problem is intrinsically three-dimensional
In his 1957 paper [1] L. Dubins considered the problem of finding shortest differentiable arcs in the plane with curvature bounded by a constant and prescribed initial and terminal positions and tangents. One can generalize this problem to non-euclidean manifolds as well as to higher dimensions (cf. [15]). Considering that the boundary data - initial and terminal position and tangents - are genuinely three-dimensional, it seems natural to ask if the n-dimensional problem always reduces to the...