Spectral properties of the adjoint operator and applications.
Spectral theory of translation surfaces : A short introduction
We define translation surfaces and, on these, the Laplace operator that is associated with the Euclidean (singular) metric. This Laplace operator is not essentially self-adjoint and we recall how self-adjoint extensions are chosen. There are essentially two geometrical self-adjoint extensions and we show that they actually share the same spectrum
Spectre asymptotique du revêtement universel des tores
Spectre d'une variété privée d'un ɛ-tube (Conditions de Dirichlet)
Spectrum of twisted Dirac operators on the complex projective space
In this paper, we explicitly determine the spectrum of Dirac operators acting on smooth sections of twisted spinor bundles over the complex projective space for .
Stabilité de l'inégalité de Faber-Krahn en courbure de Ricci positive
P. Bérard et D. Meyer ont démontré une inégalité du type Faber-Krahn pour les domaines d'une variété compacte à courbure de Ricci positive. Nous démontrons des résultats de stabilité associés à cette inégalité.
Stabilité des applications différentiables
Stabilité simultanée de deux fonctions différentiables
Nous caractérisons les couples de fonctions différentiables , définies sur une variété compacte de dimension , qui sont simultanément stables en ce sens que, pour tout couple assez voisin, il existe un difféomorphisme de et deux difféomorphismes et de tels que et échangent et alors que et échangent et . L’outil essentiel est une technique de résolution des équations du type où les inconnues et sont des fonctions de classe .
Stability of Caustics.
Stability of Critical Points under Small Perturbations. Part II: Analytic Theory.
Stability of Critical Points under Small Perturbations. Part I: Topological Theory.
Stability of Critical Values and Isolated Critical Continua.
Stability of the Cut Locus in Dimensions Less Than or Equal to 6.
Stable mappings of 3-manifolds into the plane
Stable surfaces in Euclidean three space.
Stochastic differential inclusions of Langevin type on Riemannian manifolds
We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
Stokes' phenomenon; smoothing a victorian discontinuity
Stratifications of polynomial spaces
In the paper we construct some stratifications of the space of monic polynomials in real and complex cases. These stratifications depend on properties of roots of the polynomials on some given semialgebraic subset of R or C. We prove differential triviality of these stratifications. In the real case the proof is based on properties of the action of the group of interval exchange transformations on the set of all monic polynomials of some given degree. Finally we compare stratifications corresponding...
Strict differentiability via differentiability
Strong density for higher order Sobolev spaces into compact manifolds
Given a compact manifold , an integer and an exponent , we prove that the class of smooth maps on the cube with values into is dense with respect to the strong topology in the Sobolev space when the homotopy group of order is trivial. We also prove density of maps that are smooth except for a set of dimension , without any restriction on the homotopy group of .