Plateau's Problem for surfaces of constant mean curvature form a global point of view.
Plateau-Stein manifolds
We study/construct (proper and non-proper) Morse functions f on complete Riemannian manifolds X such that the hypersurfaces f(x) = t for all −∞ < t < +∞ have positive mean curvatures at all non-critical points x ∈ X of f. We show, for instance, that if X admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
Plongements lipschitziens dans un espace pentagonal
Poincaré-invariant structures in the solution manifold of a nonlinear wave equation.
The solution manifold M of the equation ⎯φ + gφ3 = 0 in Minkowski space is studied from the standpoint of the establishment of differential-geometric structures therein. It is shown that there is an almost Kähler structure globally defined on M that is Poincaré invariant. In the vanishing curvature case g = 0 the structure obtained coincides with the complex Hilbert structure in the solution manifold of the real wave equation. The proofs are based on the transfer of the equation to an ambient universal...
Product preserving functors of infinite dimensional manifolds.
Product preserving functors of infinite-dimensional manifolds
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of -algebras.
Projective bundles on infinite-dimensional complex spaces.
Projective limits of Banach vector bundles.
Property Z and Property Y sets in F-manifolds
Propriété de Runge et enveloppe d'holomorphie de certaines variétés analytiques de dimensions infinies
Pseudo-interiors of hyperspaces
Quantum 4-sphere: the infinitesimal approach
We describe how the constructions of quantum homogeneous spaces using infinitesimal invariance and quantum coisotropic subgroups are related. As an example we recover the quantum 4-sphere of [2] through infinitesimal invariance with respect to .
Quantum field theory in a non-commutative space: theoretical predictions and numerical results on the fuzzy sphere.
Quantum gravity: unification of principles and interactions, and promises of spectral geometry.
Quantum isometry group for spectral triples with real structure.
Quantum spacetime: a disambiguation.
Quantum ultrametrics on AF algebras and the Gromov-Hausdorff propinquity
We construct quantum metric structures on unital AF algebras with a faithful tracial state, and prove that for such metrics, AF algebras are limits of their defining inductive sequences of finite-dimensional C*-algebras for the quantum propinquity. We then study the geometry, for the quantum propinquity, of three natural classes of AF algebras equipped with our quantum metrics: the UHF algebras, the Effrös-Shen AF algebras associated with continued fraction expansions of irrationals, and the Cantor...
Reconstruction of manifolds and subsets of normed spaces from subgroups of their homeomorphism groups [Book]
Regular infinite dimensional Lie groups.
Régularité des solutions d'équations aux dérivées partielles non linéaires associées à un système de champs de vecteurs
Cet article considère des équations aux dérivées partielles non linéaires de la forme , , où les sont des champs de vecteur vérifiant la condition de Hörmander. Soit une solution réelle de classe ; on suppose que la localisation de l’opérateur linéarisé sur le groupe de Lie associé au système est hypoelliptique; nous démontrons sous ces hypothèses que est de classe .