Resolutions of -stratifolds with isolated singularities.
Resolvent at low energy and Riesz transform for Schrödinger operators on asymptotically conic manifolds. II
Let be a complete noncompact manifold of dimension at least 3 and an asymptotically conic metric on , in the sense that compactifies to a manifold with boundary so that becomes a scattering metric on . We study the resolvent kernel and Riesz transform of the operator , where is the positive Laplacian associated to and is a real potential function smooth on and vanishing at the boundary.In our first paper we assumed that has neither zero modes nor a zero-resonance and showed...
Résonances
Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres
It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2) and it is...
Restriction de la distance géodésique à un arc et rigidité
Restrictions of smooth functions to a closed subset
We first provide an approach to the conjecture of Bierstone-Milman-Pawłucki on Whitney’s problem on extendability of functions. For example, the conjecture is affirmative for classical fractal sets. Next, we give a sharpened form of Spallek’s theorem on flatness.
Restrictive metric regularity and generalized differential calculus in Banach spaces.
Résultats nouveaux a propos des conjectures de Lichnerowicz et de Carathéodory
Résurgence d'un thème de Huygens-Fresnel
Revisiting the construction of gap functions for variational inequalities and equilibrium problems via conjugate duality
Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...
Ricci and Bianchi identities for -normal -linear connections on .
Ricci curvature and qusiconformal deformations of a Riemannian manifold.
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 ...
Riemann map and holomorphic dynamics.
Riemannian geometries on spaces of plane curves
We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from to the plane modulo the group of diffeomorphisms of , acting as reparametrizations. In particular we investigate the metric, for a constant , where is the curvature of the curve and , are normal vector fields to . The term is a sort of geometric Tikhonov regularization because, for , the geodesic distance between any two distinct curves is 0, while for the...
Riemannian structures and -homology. (Structures riemanniennes et -homologie.)
Riemannian manifolds whose Laplacians have purely continuous spectrum.
Riemannian manifolds with maximal eigenfunction growth
Riemannian structures on higher order frame bundles over Riemannian manifolds.