Magnetic Curves in a Euclidean Space: One Example, Several Approaches
Magnetic flows and Gaussian thermostats on manifolds of negative curvature
We consider a class of flows which includes both magnetic flows and Gaussian thermostats of external fields. We give sufficient conditions for such flows on manifolds of negative sectional curvature to be Anosov.
Mainfolds with small excess and bounded curvature.
Manifolds admitting stable forms
In this note we give a direct method to classify all stable forms on as well as to determine their automorphism groups. We show that in dimensions 6, 7, 8 stable forms coincide with non-degenerate forms. We present necessary conditions and sufficient conditions for a manifold to admit a stable form. We also discuss rich properties of the geometry of such manifolds.
Manifolds carrying bounded quasiharmonic but no bounded harmonic functions.
Manifolds of almost nonnegative curvature
Manifolds of Dimension 3 with Prescribed Positive Curvature and with Nontrivial Homology.
Manifolds of nonpositive curvature and their buildings
Manifolds with Geodesic Chords of Constant Length.
Manifolds with quadratic curvature decay and slow volume growth
Manifolds with singularities accepting a metric of positive scalar curvature.
Manifolds with strong harmonic boundaries but without Green's functions of clamped bodies
Manifolds with wells of negative curvature (with an Appendix by Daniel Ruberman).
Manifolds without Conjugate Points.
Maps between almost Kähler manifolds and framed -manifolds.
Maps of manifolds with indefinite metrics preserving certain geometrical entities.
Margulis Lemma, entropy and free products
We prove a Margulis’ Lemma à la Besson-Courtois-Gallot, for manifolds whose fundamental group is a nontrivial free product , without 2-torsion. Moreover, if is torsion-free we give a lower bound for the homotopy systole in terms of upper bounds on the diameter and the volume-entropy. We also provide examples and counterexamples showing the optimality of our assumption. Finally we give two applications of this result: a finiteness theorem and a volume estimate for reducible manifolds.
Martin boundary for homogeneous riemannian manifolds of negative curvature at the bottom of the spectrum.
In this paper we treat noncoercive operators on simply connected homogeneous manifolds of negative curvature.
Maslov indices on the metaplectic group
We use the properties of to construct functions associated with the elements of the lagrangian grassmannian (n) which generalize the Maslov index on Mp(n) defined by J. Leray in his “Lagrangian Analysis”. We deduce from these constructions the identity between and a subset of , equipped with appropriate algebraic and topological structures.
Mass endomorphism, surgery and perturbations
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.