Réarrangements des difféomorphismes sur une variété compacte mesurée
Recursions of symmetry orbits and reduction without reduction.
Refined Kato inequalities in riemannian geometry
We describe the recent joint work of the author with David M. J. Calderbank and Paul Gauduchon on refined Kato inequalities for sections of vector bundles living in the kernel of natural first-order elliptic operators.
Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings
In this paper we study the lower semicontinuous envelope with respect to the -topology of a class of isotropic functionals with linear growth defined on mappings from the -dimensional ball into that are constrained to take values into a smooth submanifold of .
Relaxation of isotropic functionals with linear growth defined on manifold constrained Sobolev mappings
In this paper we study the lower semicontinuous envelope with respect to the L1-topology of a class of isotropic functionals with linear growth defined on mappings from the n-dimensional ball into that are constrained to take values into a smooth submanifold of .
Resolvent Flows for Convex Functionals and p-Harmonic Maps
We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such functions as the large time limit of the resolvents, which generalizing pioneering work by Jost for convex functionals on complete CAT(0)-spaces. The results can be applied to Lp-Wasserstein space over complete p-uniformly convex spaces. As an application,...
Ricci flow coupled with harmonic map flow
We investigate a coupled system of the Ricci flow on a closed manifold with the harmonic map flow of a map from to some closed target manifold ,where is a (possibly time-dependent) positive coupling constant. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of a-priori by choosing large enough. Moreover, it suffices to bound the curvature of to also obtain control of ...
Riemannian convexity.
Riemannian manifolds with almost constant scalar curvature.
Rigidity and cohomology of hyperbolic manifolds
When is a real hyperbolic manifold, it is already known that if the critical exponent is small enough then some cohomology spaces and some spaces of harmonic forms vanish. In this paper, we show rigidity results in the borderline case of these vanishing results.
Rigidity in non-negative curvature
Rigidity of Einstein manifolds and generalized quasi-Einstein manifolds
We discuss the rigidity of Einstein manifolds and generalized quasi-Einstein manifolds. We improve a pinching condition used in a theorem on the rigidity of compact Einstein manifolds. Under an additional condition, we confirm a conjecture on the rigidity of compact Einstein manifolds. In addition, we prove that every closed generalized quasi-Einstein manifold is an Einstein manifold provided μ = -1/(n-2), λ ≤ 0 and β ≤ 0.
Rigidity of generalized laplacians and some geometric applications. (Summary).
Rigidity of generalized laplacians and some geometric applications.
Rigidity of noncompact manifolds with cyclic parallel Ricci curvature
We prove that if M is a complete noncompact Riemannian manifold whose Ricci tensor is cyclic parallel and whose scalar curvature is nonpositive, then M is Einstein, provided the Sobolev constant is positive and an integral inequality is satisfied.
Rough isometries and p-harmonic functions with finite Dirichlet integral.