Alberto Candel

The harmonic measures of Lucy Garnett

Abstract This paper presents an improved approach to the theory of harmonic measures for foliated spaces introduced by Garnett. This approach is based on a method for solving elliptic equations on foliated spaces and on the Hille–Yosida theory. The diffusion semigroup of a general Laplacian and its infinitesimal generator are made explicit. Applications of the path space to the dynamical study of a foliated space are described. In particular, the final section studies cocycles on foliated spaces, a formula for their asymptotic limit, and some analytic and geometric consequences.

Gromov's Centralizer Theorem

AbstractWe study the properties of rigid geometric structures and their relation with those of finite type. The main result proves that for a noncompact simple Lie group G acting analytically on a manifold M preserving a finite volume and either a connection or a geometric structure of finite type there is a nontrivial space of globally defined Killing vector fields on the universal cover

Generic coarse geometry of leaves

\tilde M

Some Examples of First Exit Times

that centralize the action of G. Several appplications of this result are provided.

Nonreduction of Relations in the Gromov Space to Polish Actions

This paper gives an upper bound for the first eigenvalue of the universal cover of a complete, stable minimal surface in hyperbolic space, and a sharper one for least area disks.

Examples and Open Problems

In this chapter we recall basic concepts and preliminaries about foliated spaces, as well as fix the notation, so that the foliated space versions of our main theorems follow directly from their pseudogroup versions.

Coarse Quasi-Isometries

This paper extends the theory of turbulence of Hjorth to certain classes of equivalence relations that cannot be induced by Polish actions. It applies this theory to analyze the quasi-isometry relation and finite Gromov-Hausdorff distance relation in the space of isometry classes of pointed proper metric spaces, called the Gromov space.

Higson Corona and Asymptotic Dimension

The purpose of this article is to compute the expected first exit times of Brownian motion from a variety of domains in the Euclidean plane and in the hyperbolic plane.