Geodesic algorithms in Riemannian geometry.
Geodesic Mappings on Compact Riemannian Manifolds with Conditions on Sectional Curvature
Geometric dynamics of calcium oscillations ODEs systems.
Geometric methods for solving Codazzi and Monge-Ampère equations.
Geometric P.D.E.'s with isolated singularities.
Géométrie conforme en dimension : ce que l’analyse nous apprend
Cet article présente les idées, les outils et les résultats qui ont permis à Chang S.-Y. A., M. Gursky et Yang P. de donner une caractérisation intégrale conforme de la sphère standard en dimension 4. Nous démarrons avec une généralisation à cette dimension de la formule de Polyakov pour les déterminants régularisés, que nous utilisons ensuite pour résoudre des problèmes du type “Yamabe” pour des polynômes quadratiques en la courbure de Ricci. Nous introduisons au passage le concept de paire conforme,...
Geometrische Methoden zur Gewinnung von A-Priori-Schranken für harmonische Abbildungen.
Geometry of Kähler metrics and foliations by holomorphic discs
Gradient estimates for inverse curvature flows in hyperbolic space
We prove gradient estimates for hypersurfaces in the hyperbolic space Hn+1, expanding by negative powers of a certain class of homogeneous curvature functions F. We obtain optimal gradient estimates for hypersurfaces evolving by certain powers p > 1 of F-1 and smooth convergence of the properly rescaled hypersurfaces. In particular, the full convergence result holds for the inverse Gauss curvature flow of surfaces without any further pinching condition besides convexity of the initial hypersurface....
Graphs with prescribed mean curvature on hyperbolic spaces.
Growth of weighted volume and some applications
We define cut-off functions in order to allow higher growth for Dirichlet energy. Our results are generalizations of the classical Cheng-Yau’s growth conditions of parabolicity. Finally we give some applications to the function theory of Kähler and quaternionic-Kähler manifolds.
Hamiltonian flows of curves in and vector soliton equations of mKdV and sine-Gordon type.
Harmonic diffeomorphisms and Teichmüller theory.
Harnack inequalities for curvature flows depending on mean curvature.
Heat content asymptotics for operators to Laplace type with Neumann boundary conditions.
Hypersurfaces of constant curvature in hyperbolic space II
This is the second of a series of papers in which we investigate the problem of finding, in hyperbolic space, complete hypersurfaces of constant curvature with a prescribed asymptotic boundary at infinity for a general class of curvature functions. In this paper we focus on graphs over a domain with nonnegative mean curvature.
Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds
Given a domain of and a -dimensional non-degenerate minimal submanifold of with , we prove the existence of a family of embedded constant mean curvature hypersurfaces in which as their mean curvature tends to infinity concentrate along and intersecting perpendicularly along their boundaries.
Inégalité isopérimétrique en dimension 3 d'après B. Kleiner
Inégalités de Sobolev optimales et inégalités isopérimétriques sur les variétés
Interior estimates for solutions of Abreu's equation.
This paper develops various estimates for solutions of a nonlinear, fouth order PDE which corresponds to prescribing the scalar curvature of a toric Kähler metric. The results combine techniques from Riemannian geometry and from the theory of Monge-Ampère equations.