Mean curvature functions of codimension-one foliations. II.
Mean curvature vector and symplectic topology of Lagrangian submanifolds in Einstein-Kähler manifolds.
Means in complete manifolds: uniqueness and approximation
Let M be a complete Riemannian manifold, M ∈ ℕ and p ≥ 1. We prove that almost everywhere on x = (x1,...,xN) ∈ MN for Lebesgue measure in MN, the measure μ ( x ) = 1 N ∑ k = 1 N δ x k has a uniquep–mean ep(x). As a consequence, if X = (X1,...,XN) is a MN-valued random variable with absolutely continuous law, then almost surely μ(X(ω)) has a unique p–mean. In particular if (Xn)n ≥ 1 is an independent sample of an absolutely continuous law in M, then the process ep,n(ω) = ep(X1(ω),...,Xn(ω)) is...
Measured geodesic laminations in Flatland
Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure (that is a singular flat surface with holonomy ), called flat laminations, and we define transverse measures on flat laminations similar to transverse measures on hyperbolic laminations, taking into account that the images of the leaves of a flat lamination are in...
Measures on the geometric limit set in higher rank symmetric spaces
Measures representable as -dimensional Hausdorff measures
Meilleures constantes dans le théorème d'inclusion de Sobolev
Meilleures constantes et inégalités de Sobolev optimales sur les variétés riemanniennes compactes
Mesure harmonique et mesure de Bowen-Margulis
Mesures de courbure des variétés lisses et des polyèdres
Metaplectic quantization of the moduli spaces of flat and parabolic bundles.
Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet
Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet
Consider a sub-riemannian geometry(U,D,g) where U is a neighborhood of 0 in R3, D is a Martinet type distribution identified to ker ω, ω being the 1-form: , q=(x,y,z) and g is a metric on D which can be taken in the normal form: , a=1+yF(q), c=1+G(q), . In a previous article we analyze the flat case: a=c=1; we describe the conjugate and cut loci, the sphere and the wave front. The objectif of this article is to provide a geometric and computational framework to analyze the general case....
Metric Circles and Bisectors.
Metric constraints on exotic spheres via Alexandrov geometry.
Metric Entropy of Homogeneous Spaces
For a precompact subset K of a metric space and ε > 0, the covering number N(K,ε) is defined as the smallest number of balls of radius ε whose union covers K. Knowledge of the metric entropy, i.e., the asymptotic behaviour of covering numbers for (families of) metric spaces is important in many areas of mathematics (geometry, functional analysis, probability, coding theory, to name a few). In this paper we give asymptotically correct estimates for covering numbers for a large class of homogeneous...
Metric minimizing surfaces.
Metric of special 2F-flat Riemannian spaces
In this paper we find the metric in an explicit shape of special -flat Riemannian spaces , i.e. spaces, which are -planar mapped on flat spaces. In this case it is supposed, that is the cubic structure: .
Metric Perspectives of the Ricci Flow Applied to Disjoint Unions
In this paper we consider compact, Riemannian manifolds M1, M2 each equipped with a oneparameter family of metrics g1(t), g2(t) satisfying the Ricci flow equation. Adopting the characterization of super-solutions to the Ricci flow developed by McCann-Topping, we define a super Ricci flow for a family of distance metrics defined on the disjoint union M1 ⊔ M2. In particular, we show such a super Ricci flow property holds provided the distance function between points in M1 and M2 is itself a super...
Metric Ricci Curvature and Flow for PL Manifolds
We summarize here the main ideas and results of our papers [28], [14], as presented at the 2013 CIRM Meeting on Discrete curvature and we augment these by bringing up an application of one of our main results, namely to solving a problem regarding cube complexes.