We study the stable norm on the first homology of a closed non-orientable surface equipped with a Riemannian metric. We prove that in every conformal class there exists a metric whose stable norm is polyhedral. Furthermore the stable norm is never strictly convex if the first Betti number of the surface is greater than two.
Let (M,d) be a metric space with a fixed origin O. P. Lévy defined Brownian motion X(a); a ∈ M as 0. X(O) = 0. 1. X(a) - X(b) is subject to the Gaussian law of mean 0 and variance d(a,b). He gave an example for , the m-dimensional sphere. Let be the Gaussian random measure on , that is, 1. Y(B) is a centered Gaussian system, 2. the variance of Y(B) is equal of μ(B), where μ is the uniform measure on , 3. if B₁ ∩ B₂ = ∅ then Y(B₁) is independent of Y(B₂). 4. for , i = 1,2,..., , i ≠ j, we...
In this paper, we study the stability of space-like hypersurfaces with constant scalar curvature immersed in the de Sitter spaces.
Some new examples of standard homogeneous Einstein manifolds with semisimple transitive groups of motions and semisimple isotropy subgroups are constructed. For the construction of these examples the solutions of some systems of Diophantine equations are used.
The notion of a local line bundle on a manifold, classified by 2-cohomology with real coefficients, is introduced. The twisting of pseudodifferential operators by such a line bundle leads to an algebroid with elliptic elements with real-valued index, given by a twisted variant of the Atiyah-Singer index formula. Using ideas of Boutet de Monvel and Guillemin the corresponding twisted Toeplitz algebroid on any compact symplectic manifold is shown to yield the star products...
Dans cet article nous rappelons la définition d’un star-produit, et étudions et classifions les star-produits sur un fibré cotangent complexe. Ce sujet a fait l’objet d’une conférence en l’honneur de V. Guillemin en septembre 1998 ; il est dévelopé plus en détail dans [2]. Cet article est dédié à la mémoire de M. Flato et A. Lichnerowicz, disparus peu de temps après la conférence, et qui ont grandement contribué au sujet.
In this paper we show that the windings of geodesics around the cusps of a Riemann surface of a finite area, behave asymptotically as independent Cauchy variables.