Complex geometry of generalized annuli.
Conjugate-cut loci and injectivity domains on two-spheres of revolution
In a recent article [B. Bonnard, J.-B. Caillau, R. Sinclair and M. Tanaka, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 26 (2009) 1081–1098], we relate the computation of the conjugate and cut loci of a family of metrics on two-spheres of revolution whose polar form is g = dϕ2 + m(ϕ)dθ2 to the period mapping of the ϕ-variable. One purpose of this article is to use this relation to evaluate the cut and conjugate loci for a family of metrics arising as a deformation of the round sphere and to determine...
Contributions of rational homotopy theory to global problems in geometry
Convergence of Bergman geodesics on
The space of Kähler metrics in a fixed Kähler class on a projective Kähler manifold is an infinite dimensional symmetric space whose geodesics are solutions of a homogeneous complex Monge-Ampère equation in , where is an annulus. Phong-Sturm have proven that the Monge-Ampère geodesic of Kähler potentials of may be approximated in a weak sense by geodesics of the finite dimensional symmetric space of Bergman metrics of height . In this article we prove that in in the case of...
Convex Surfaces Whose Geodesics Are Planar.
Cordes et géodésiques fermées
Correspondances géodésiques entre les surfaces euclidiennes à singularités coniques.
A. J. Montesinos has shown that a geodesic correspondence between two complete Riemannian manifolds with transitive topological geodesic flow is a homothety. In this paper we prove a similar result for a conformal geodesic correspondence between two singular flat surfaces with conical singularities and negative concentrated curvature.
Cut loci of closed surfaces without conjugate points
Cut locus and parallel circles of a closed curve on a Riemannian plane admitting total curvature.
Dans le fibré de l'espace des lacets libres, la fibre n'est pas, en général, totalement non cohomologue a zéro.
Deformations of Metrics and Biharmonic Maps
We construct biharmonic non-harmonic maps between Riemannian manifolds and by first making the ansatz that be a harmonic map and then deforming the metric on by to render biharmonic, where is a smooth function with gradient of constant norm on and . We construct new examples of biharmonic non-harmonic maps, and we characterize the biharmonicity of some curves on Riemannian manifolds.
Dénombrement des géodésiques fermées sur certaines variétés avec pointes
Des métriques finslériennes sur le disque à partir d'une fonction distance entre les points.
Determination of metrics by boundary energy.
Deux généralisation du «théorèm des trois cercles» de Hadamard.
Deviations of stationary curves in the bundle .
Diastolic and isoperimetric inequalities on surfaces
We prove a universal inequality between the diastole, defined using a minimax process on the one-cycle space, and the area of closed Riemannian surfaces. Roughly speaking, we show that any closed Riemannian surface can be swept out by a family of multi-loops whose lengths are bounded in terms of the area of the surface. This diastolic inequality, which relies on an upper bound on Cheeger’s constant, yields an effective process to find short closed geodesics on the two-sphere, for instance. We deduce...
Dichtepunkte im Spektrum Riemannscher Flächen.
Die Parametrisierung des Teichmüllerraumes durch geodätische Längenfunktionen.
Diffeomorphisms of the Circle and Geodesic Fields on Riemannian Surfaces of Genus One.