Harmonic measures versus quasiconformal measures for hyperbolic groups

Quasiconformal Distortion of Hausdorff Measures

In this paper we prove that if φ : C → C is a K-quasiconformal map, 0 < t < 2, and E ⊂ C is a compact set contained in a ball B, then H(E) diam(B) ≤ C(K) ( H ′ (φ(E)) diam(φ(B))t′ ) t tK

Harmonic Superspace, Minimal Unitary Representations and Quasiconformal Groups

We show that there is a remarkable connection between the harmonic superspace (HSS) formulation of N = 2, d = 4 supersymmetric quaternionic Kähler sigma models that couple to N = 2 supergravity and the minimal unitary representations of their isometry groups. In particular, for N = 2 sigma models with quaternionic symmetric target spaces of the form G/H × SU(2) we establish a one-to-one mapping...

Physical Measures for Partially Hyperbolic Surface Endomorphisms

We consider dynamical systems generated by partially hyperbolic surface endomorphisms of class Cr with one-dimensional strongly unstable subbundle. As the main result, we prove that such a dynamical system generically admits finitely many ergodic physical measures whose union of basins of attraction has total Lebesgue measure, provided that r ≥ 19.

SRB measures for certain almost hyperbolic diffeomorphisms

Scaling Properties of Hyperbolic Measures

In this article we consider a class of maps which includes C 1+ diieomorphisms as well as invertible and nonivertible maps with piecewise smooth singularities. We prove a general scaling result for any hyperbolic measure which is invariant for a map from our class. The existence of the pointwise dimension and the Brin-Katok local entropy formula are special cases of our scaling result.