Martingales on noncompact manifolds : maximal inequalities and prescribed limits
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.
Matched pairs of topological Lie algebras corresponding to Lie bialgebra structures on and
Mathematical modelling of cable stayed bridges: existence, uniqueness, continuous dependence on data, homogenization of cable systems
A model of a cable stayed bridge is proposed. This model describes the behaviour of the center span, the part between pylons, hung on one row of cable stays. The existence, the uniqueness of a solution of a time independent problem and the continuous dependence on data are proved. The existence and the uniqueness of a solution of a linearized dynamic problem are proved. A homogenizing procedure making it possible to replace cables by a continuous system is proposed. A nonlinear dynamic problem connected...
Matrices carrées sur l'algèbre de Weyl
Matrix Integrals, Toda Symmetries, Virasoro Constraints and Orthogonal Polynomials
Maximal functions related to subelliptic operators invariant under an action of a nilpotent Lie group
Maximal functions related to subelliptic operators invariant under an action of a solvable Lie group
On the domain S_a = {(x,e^b): x ∈ N, b ∈ ℝ, b > a} where N is a simply connected nilpotent Lie group, a certain N-left-invariant, second order, degenerate elliptic operator L is considered. N × {e^a} is the Poisson boundary for L-harmonic functions F, i.e. F is the Poisson integral F(xe^b) = ʃ_N f(xy)dμ^b_a(x), for an f in L^∞(N). The main theorem of the paper asserts that the maximal function M^a f(x) = sup{|ʃf(xy)dμ_a^b(y)| : b > a} is of weak type (1,1).
Maximal functions related to subelliptic operators with polynomially growing coefficients.
Maximal ideals in the Lie algebra of vector fields
Maximal regularity and Hardy spaces
Maximale eindeutige Lösungen (Riemannsche Flächen) für Cauchysche Anfangswertaufgaben bei partiellen Differentialgleichungssystemen erster Ordnung für eine gesuchte Funktion auf C°°-Mannigfaltigkeiten I.
Maximale eindeutige Lösungen (Riemannsche Flächen) für Cauchysche Anfangswertaufgaben bei partiellen Differentialgleichungssystemen erster Ordnung für eine gesuchte Funktion auf C°°-Mannigfaltigkeiten. III.
Maximale eindeutige Lösungen (Riemannsche Flächen) für Cauchysche Anfangswertaufgaben bei partiellen Differentialgleichungssystemen erster Ordnung für eine gesuchte Funktion auf C°°-Mannigfaltigkeiten II.
Maximally degenerate laplacians
The Laplacian of a compact Riemannian manifold is called maximally degenerate if its eigenvalue multiplicity function is of maximal growth among metrics of the same dimension and volume. Canonical spheres and CROSSes are MD, and one asks if they are the only examples. We show that a MD metric must be at least a Zoll metric with just one distinct eigenvalue in each cluster, and hence with all band invariants equal to zero. The principal band invariant is then calculated in terms of geodesic...
Maximum principles and minimal surfaces
Mean curvature and the heat equation.
Mean curvature functions of codimension-one foliations.
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...
Mean-value theorems and ergodicity of certain geodesic random walks