Harmonicity of Quasiconformal Measures and Poisson Boundaries of Hyperbolic Spaces

some properties of fuzzy hilbert spaces and norm of operators

in this thesis, at first we investigate the bounded inverse theorem on fuzzy normed linear spaces and study the set of all compact operators on these spaces. then we introduce the notions of fuzzy boundedness and investigate a new norm operators and the relationship between continuity and boundedness. and, we show that the space of all fuzzy bounded operators is complete. finally, we define...

Harmonicity of Gibbs Measures

In this paper we extend the construction of random walks with a prescribed Poisson boundary found in [CM04] to the case of measures in the class of a generalized Gibbs state. The price for dropping the α-quasiconformal assumptions is that we must restrict our attention to CAT(−κ) groups. Apart from the new estimates required, we prove a new approximation scheme to provide a positive basis for p...

Poisson kernels of half–spaces in real hyperbolic spaces

We provide an integral formula for the Poisson kernel of half-spaces for Brownian motion in real hyperbolic space Hn. This enables us to find asymptotic properties of the kernel. Our starting point is the formula for its Fourier transform. When n = 3, 4 or 6 we give an explicit formula for the Poisson kernel itself. In the general case we give various asymptotics and show convergence to the Poi...

Identities on hyperbolic manifolds and quasiconformal homogeneity of hyperbolic surfaces

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