A Morse theory for light rays on stably causal lorentzian manifolds
A new characterization of -stable hypersurfaces in space forms
In this paper we study the -stability of closed hypersurfaces with constant -th mean curvature in Riemannian manifolds of constant sectional curvature. In this setting, we obtain a characterization of the -stable ones through of the analysis of the first eigenvalue of an operator naturally attached to the -th mean curvature.
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...
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. Part III : Petrov type III space-times
An explicit determination of the space-times on which the conformally invariant scalar wave equation satisfies Huygens' principle. — Part II : Petrov type D space-times
Averaging problem in general relativity and cosmology