Spinc-quantization and the K-multiplicities of the discrete series
Splitting the spectral flow and the Alexander matrix.
Stability results for Harnack inequalities
We develop new techniques for proving uniform elliptic and parabolic Harnack inequalities on weighted Riemannian manifolds. In particular, we prove the stability of the Harnack inequalities under certain non-uniform changes of the weight. We also prove necessary and sufficient conditions for the Harnack inequalities to hold on complete non-compact manifolds having non-negative Ricci curvature outside a compact set and a finite first Betti number or just having asymptotically...
Stable minimal cones in and with constant scalar curvature.
Steady-state bifurcations of the three-dimensional Kolmogorov problem.
Stochastic calculus and martingales on trees
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.
Stochastic methods and differential geometry
Stochastic parallel transport and connections of
In this paper we prove that there is a bijective correspondence between connections of , the principal bundle of the second order frames of , and stochastic parallel transport in the tangent space of . We construct in a direct geometric way a prolongation of connections without torsion of to connections of . We interpret such prolongation in terms of stochastic calculus.
Stochastic processes and antiderivational equations on non-Archimedean manifolds.
Stochastic Taylor expansions and heat kernel asymptotics
These notes focus on the applications of the stochastic Taylor expansion of solutions of stochastic differential equations to the study of heat kernels in small times. As an illustration of these methods we provide a new heat kernel proof of the Chern–Gauss–Bonnet theorem.
Strichartz estimates for the wave equation on manifolds with boundary
Strichartz inequalities for Lipschitz metrics on manifolds and nonlinear Schrödinger equation on domains
We prove wellposedness of the Cauchy problem for the nonlinear Schrödinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on manifolds with Lipschitz metric.
Strichartz inequalities for the Schrödinger equation with the full Laplacian on the Heisenberg group
We prove Strichartz inequalities for the solution of the Schrödinger equation related to the full Laplacian on the Heisenberg group. A key point consists in estimating the decay in time of the norm of the free solution; this requires a careful analysis due also to the non-homogeneous nature of the full Laplacian.
Strong boundary values : independence of the defining function and spaces of test functions
The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics.
Structure of second-order symmetric Lorentzian manifolds
, that is to say, Lorentzian manifolds with vanishing second derivative of the curvature tensor , are characterized by several geometric properties, and explicitly presented. Locally, they are a product where each factor is uniquely determined as follows: is a Riemannian symmetric space and is either a constant-curvature Lorentzian space or a definite type of plane wave generalizing the Cahen–Wallach family. In the proper case (i.e., at some point), the curvature tensor turns out to...
Structure of symmetry groups via Cartan's method: survey of four approaches.
Study of exponential stability of coupled wave systems via distributed stabilizer.
Sublinear eigenvalue problems on compact Riemannian manifolds with applications in Emden-Fowler equations
Let (M,g) be a compact Riemannian manifold without boundary, with dim M ≥ 3, and f: ℝ → ℝ a continuous function which is sublinear at infinity. By various variational approaches, existence of multiple solutions of the eigenvalue problem , σ ∈ M, ω ∈ H₁²(M), is established for certain eigenvalues λ > 0, depending on further properties of f and on explicit forms of the function K̃. Here, stands for the Laplace-Beltrami operator on (M,g), and α, K̃ are smooth positive functions. These multiplicity...
Submersions and equivariant Quillen metrics
In this paper, we calculate the behaviour of the equivariant Quillen metric by submersions. We thus extend a formula of Berthomieu-Bismut to the equivariant case.