A splitting theorem for open nonnegatively curved manifolds.
A splitting theorem for spaces of nonpositive curvature.
A stable class of spacetimes with naked singularities
We present a stable class of spacetimes which satisfy the conditions of the singularity theorem of Hawking & Penrose (1970), and which contain naked singularities. This offers counterexamples to a geometric version of the strong cosmic censorship hypothesis.
A stable classification of Lefschetz fibrations.
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 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 strong minimax property of nondegenerate minimal submanifolds.
A structure by conformal transformations of Finsler functions on the projectivized tangent bundle of Finsler spaces with the Chern connection.
A study on the one parameter Lorentzian spherical motions.
A Study on -recurrence -curvature tensor in -contact metric manifolds
In this paper we study -recurrence -curvature tensor in-contact metric manifolds.
A subsidiary variational problem and existence criteria for capillary surfaces.
A Sufficient Condition for a Compact Immersion to be Spherical.
A sufficient condition for the convexity of the area of an isoptic curve of an oval
A surface in a space with projective connexion
A surface which has a family of geodesics of curvature.
A survey of boundary value problems for bundles over complex spaces
Let be a reduced -dimensional complex space, for which the set of singularities consists of finitely many points. If denotes the set of smooth points, the author considers a holomorphic vector bundle , equipped with a Hermitian metric , where represents a closed analytic subset of complex codimension at least two. The results, surveyed in this paper, provide criteria for holomorphic extension of across , or across the singular points of if . The approach taken here is via the metric...
A survey on axioms of submanifolds in Riemannian and Kaehlerian geometry
A survey on Nambu-Poisson brackets.
A survey on the Hawking – Penrose theory
A Symbolic Dynamics for Geodesics on Punctured Riemann Surfaces.