Sabinin‘s method for classification of local Bol loops
Saddle Points and Multiple Solutions of Differential Equations.
Scalar curvature, covering spaces, and Seiberg-Witten theory.
Scalar curvature of defineable CAT-spaces.
Scalar differential invariants of symplectic Monge-Ampère equations
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allow us to construct numerous scalar differential invariants...
Scattering and resolvent on geometrically finite hyperbolic manifolds with rational cusps
These notes summarize the papers [8, 9] on the analysis of resolvent, Eisenstein series and scattering operator for geometrically finite hyperbolic quotients with rational non-maximal rank cusps. They complete somehow the talk given at the PDE seminar of Ecole Polytechnique in october 2005.
Scattering matrix for asymptotically euclidean manifolds
Scattering matrix in conformal geometry
Scattering poles for connected sums of euclidean space and Zoll manifolds
Schiffer problem and isoparametric hypersurfaces.
The Schiffer Problem as originally stated for Euclidean spaces (and later for some symmetric spaces) is the following: Given a bounded connected open set Ω with a regular boundary and such that the complement of its closure is connected, does the existence of a solution to the Overdetermined Neumann Problem (N) imply that Ω is a ball? The same question for the Overdetermined Dirichlet Problem (D). We consider the generalization of the Schiffer problem to an arbitrary Riemannian manifold and also...
Schouten tensor equations in conformal geometry with prescribed boundary metric.
Schrödinger equation spectrum and Korteweg-De Vries type invariants
Schwarzian derivative related to modules of differential operators on a locally projective manifold
We introduce a 1-cocycle on the group of diffeomorphisms Diff(M) of a smooth manifold M endowed with a projective connection. This cocycle represents a nontrivial cohomology class of Diff(M) related to the Diff(M)-modules of second order linear differential operators on M. In the one-dimensional case, this cocycle coincides with the Schwarzian derivative, while, in the multi-dimensional case, it represents its natural and new generalization. This work is a continuation of [3] where the same problems...
Schwinger terms, gerbes, and operator residues
Séances de problèmes
Second cohomology classes of the group of -flat diffeomorphisms
We study the cohomology of the group consisting of all -diffeomorphisms of the line, which are -flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group.
Second order conditions for extrema of functionals defined on regular surfaces.
Second order connections on some functional bundles
We study the second order connections in the sense of C. Ehresmann. On a fibered manifold , such a connection is a section from into the second non-holonomic jet prolongation of . Our main aim is to extend the classical theory to the functional bundle of all smooth maps between the fibers over the same base point of two fibered manifolds over the same base. This requires several new geometric results about the second order connections on , which are deduced in the first part of the paper.
Second order differentiability and Lipschitz smooth points of convex functionals
Second order differential invariants of linear frames.