Convex functionals and generalized harmonic maps into spaces of non positive curvature.
Convex functions on complete noncompact manifolds : differentiable structure
Convex Functions on Complete Noncompact Manifolds: Topological Structure.
Convex Hulls of Complete Minimal Surfaces.
Convex Immersions of Closed Surfaces in E3.
Convex isometric folding.
Convex Surfaces Whose Geodesics Are Planar.
Convexes hyperboliques et fonctions quasisymétriques
Every bounded convex open set Ω of Rm is endowed with its Hilbert metric dΩ. We give a necessary and sufficient condition, called quasisymmetric convexity, for this metric space to be hyperbolic. As a corollary, when the boundary is real analytic, Ω is always hyperbolic. In dimension 2, this condition is: in affine coordinates, the boundary ∂Ω is locally the graph of a C1 strictly convex function whose derivative is quasisymmetric.
Convexité en topologie de contact.
Convexité rationnelle des sous-variétés immergées lagrangiennes
Convexity estimates for flows by powers of the mean curvature
We study the evolution of a closed, convex hypersurface in in direction of its normal vector, where the speed equals a power of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to , depending only on and , then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere.
Convexity in combinatorial structures
Convexity of Capillary Surfaces in the Outer Space.
Convexity of Hamiltonian manifolds.
Convexity on the space of Kähler metrics
These are the lecture notes of a minicourse given at a winter school in Marseille 2011. The aim of the course was to give an introduction to recent work on the geometry of the space of Kähler metrics associated to an ample line bundle. The emphasis of the course was the role of convexity, both as a motivating example and as a tool.
Convexity Properties of the Moment Mapping.
Convexity properties of the moment mapping. II.
Convexity properties of the moment mapping. III.
Convexity theorem for isoparametric submanifolds.
Coordonnées polaires sur les surfaces riemanniennes singulières
Nous étudions les conditions sous lesquelles un point d’une surface riemannienne possède un voisinage pouvant être paramétrisé par des coordonnées polaires. Le point en question peut être un point régulier ou un point singulier conique. Nous étudions aussi la régularité de ces coordonnées polaires en fonction de la régularité de la courbure.