Abstract We prove that the hitting measure is singular with respect to Lebesgue for random walks driven by finitely supported measures on cocompact, hyperelliptic Fuchsian groups. Moreover, Hausdorff dimension of strictly less than one. Equivalently, inequality between entropy and drift strict. A similar statement proven Coxeter

a topoframe, denoted by $l_{ tau}$,  is a pair $(l, tau)$ consisting of a frame $l$ and a subframe $ tau $ all of whose elements are complementary elements in$l$. in this paper, we define and study the notions of a$tau $-real-continuous function on a frame $l$ and the set of realcontinuous functions $mathcal{r}l_tau $ as an $f$-ring.we show that $mathcal{r}l_{ tau}$is actually a generalization ...

In this paper, we show that given a set of lengths closed geodesics, there are only finitely many convex cocompact hyperbolic 3-manifolds with specified length spectrum multiplicity, homotopy equivalent to 3-manifold without handlebody factor, up orientation preserving isometries.

Background [18F]AV1451 is a commonly used radiotracer for imaging tau deposits in Alzheimer's disease (AD) and related non-AD tauopathies. Existing radiosyntheses of [18F]AV1451 require complex purifications to provide doses suitable for use in clinical imaging studies. To address this issue, we have modified the synthesis of [18F]AV1451 to use only 0.5 mg precursor, optimized the Boc-deprotect...

The energy of harmonic sections of flat bundles of nonpositively curved (NPC) length spaces over a Riemann surface S is a function Eρ on Teichmüller space TS which is a qualitative invariant of the holonomy representation ρ of π1(S). Adapting ideas of Sacks-Uhlenbeck, Schoen-Yau and Tromba, we show that the energy function Eρ is proper for any convex cocompact representation of the fundamental ...

We prove a vanishing theorem for a convex cocompact hyperbolic manifold, which relates its L cohomology and the Hausdorff dimension of its limit set. The borderline case is shown to characterize the manifold completely.

We prove a vanishing theorem for a convex cocompact hyperbolic manifold which relates its L2-cohomology and the Hausdorff dimension of its limit set. The borderline case is shown to characterize the manifold completely.

Let G be a locally compact group with cocompact connected component. We prove that the assembly map from the topological K-theory of G to the K-theory of the reduced C *-algebra of G is an isomorphism.

In this paper we study geodesic Ptolemy metric spaces X which allow proper and cocompact isometric actions of crystallographic or, more generally, virtual polycyclic groups. We show that X is equivariantly rough isometric to a Euclidean space.

Let S be a compact orientable surface, and Mod(S) its mapping class group. Then there exists a constant M(S), which depends on S, with the following property. Suppose a, b ∈ Mod(S) are independent (i.e., [a, b] 6= 1 for any n,m 6= 0) pseudo-Anosov elements. Then for any n,m ≥ M , the subgroup 〈a, b〉 is free of rank two, and convex-cocompact in the sense of Farb-Mosher. In particular all nontriv...