On the Total Absolute Curvature of Closed Curves in Manifolds of Negative Curvature.
On the volume of a unit vector field on the three-sphere.
On the Wave Equation Asymptotics of a Compact Negatively Curved Surface.
On the Wave Equation on a Compact Riemannian Manifold withour Conjugate Points.
On tori without conjugate points.
On two natural Riemannian metrics on a tube.
On Uniqueness Theoremsfor Ricci Tensor
In Riemannian geometry the prescribed Ricci curvature problem is as follows: given a smooth manifold and a symmetric 2-tensor , construct a metric on whose Ricci tensor equals . In particular, DeTurck and Koiso proved the following celebrated result: the Ricci curvature uniquely determines the Levi-Civita connection on any compact Einstein manifold with non-negative section curvature. In the present paper we generalize the result of DeTurck and Koiso for a Riemannian manifold with non-negative...
On Univalent Harmonic Maps Between Surfaces.
On Variations of Metrics.
Operators on eigenmaps between spheres
Optics in Croke-Kleiner Spaces
We explore the interior geometry of the CAT(0) spaces , constructed by Croke and Kleiner [Topology 39 (2000)]. In particular, we describe a diffraction effect experienced by the family of geodesic rays that emanate from a basepoint and pass through a certain singular point called a triple point, and we describe the shadow this family casts on the boundary. This diffraction effect is codified in the Transformation Rules stated in Section 3 of this paper. The Transformation Rules have various applications....
Optimization problems on complete Riemannian manifolds
Orthogonally pinched curvature tensors and applications.
Partages de type Borsuk
p-convex Riemannian manifolds.
Périmètre sur les variétés et application aux équations aux dérivées partielles
Petite simplification dans les groupes hyperboliques
p-harmonic functions on graphs and manifolds.
Piecewise Euclidean structures and Eberlein's rigidity theorem in the singular case.
Pincement de la première valeur propre du laplacien pour les hypersurfaces et rigidité
Robert C. Reilly a obtenu des majorations de la première valeur propre du laplacien pour les hypersurfaces de l’espace euclidien. De plus, il a montré que le cas d’égalité dans ces majorations est atteint uniquement pour les sphères géodésiques. Dans cet exposé, nous nous intéressons au problème de pincement pour ces majorations. Nous montrons que si le cas d’égalité est presque atteint, alors l’hypersurface est proche d’une sphère, en un sens que nous préciserons. Nous déduisons ensuite des résultats...