A spectral problem with an indefinite weight for an elliptic system.
A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of connections.
A stochastic approach to relativistic diffusions
A new class of relativistic diffusions encompassing all the previously studied examples has recently been introduced in the article of C. Chevalier and F. Debbasch (J. Math. Phys. 49 (2008) 043303), both in a heuristic and analytic way. A stochastic approach of these processes is proposed here, in the general framework of lorentzian geometry. In considering the dynamics of the random motion in strongly causal spacetimes, we are able to give a simple definition of the one-particle distribution function...
A stochastic characterization for harmonic morphisms.
A stochastic scheme for constructing solutions of the Schrödinger equations
A strong maximum principle for the Paneitz operator and a non-local flow for the -curvature
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert, we show...
A survey of the spectral and differential geometric aspects of the generalized de Rham-Hodge theory related with Delsarte transmutation operators in multidimension and applications to spectral and soliton problems. I.
A survey of the spectral and differential geometric aspects of the generalized De Rham-Hodge theory related with Delsarte transmutation operators in multidimension and applications to spectral and soliton problems. II.
A Twistor Correspondence for Homogeneous Polynomial Differential Operators.
A vanishing theorem for a class of Systems with simple characteristics.
A Wiener algebra for the Fefferman-Phong inequality
Abelian analytic torsion and symplectic volume
This article studies the abelian analytic torsion on a closed, oriented, Sasakian three-manifold and identifies this quantity as a specific multiple of the natural unit symplectic volume form on the moduli space of flat abelian connections. This identification computes the analytic torsion explicitly in terms of Seifert data.
Abelian coverings, Poincaré exponent of convergence and holomorphic deformations.
About a decomposition of the space of symmetric tensors of compact support on a Riemann manifold.
About Riesz transforms on the Heisenberg groups.
About the Dirac operator.
Addendum: Systems of Toda Type, Inverse Spectral Problems, and Representation Theory.
Adiabatic limits of Seifert fibrations, Dedekind sums, and the diffeomorphism type of certain 7-manifolds
As an application, we compute the Eells–Kuiper and t-invariants of certain cohomogeneity one manifolds that were studied by Dearricott, Grove, Verdiani, Wilking, and Ziller. In particular, we determine the diffeomorphism type of a new manifold of positive sectional curvature.
Algebraic study of systems of partial differential equations
Algebraic study of systems of partial differential equations