On ends of finite-volume noncompact mainfolds of nonpositive curvature

In this paper we confirm a folklore conjecture which suggests that for a complete noncompact manifold $M$ of finite volume with sectional curvature $-1 \leq K \leq 0$, if the universal cover of $M$ is a visibility manifold, then the fundamental group of each end of $M$ is almost nilpotent. Applications on the geometry and topology of noncompact nonpositively curved manifolds will be discussed.Comment: 35 pages, 2 figures. Comments are welcom

Quasinormal Modes of Self-Dual Warped AdS3_3 Black Hole in Topological Massive Gravity

We consider the various perturbations of self-dual warped AdS$_3$ black hole and obtain the exact expressions of quasinormal modes by imposing the vanishing Dirichlet boundary condition at asymptotic infinity. It is expected that the quasinormal modes agree with the poles of retarded Green's functions of the dual CFT. Our results provide a quantitative test of the warped AdS/CFT correspondence.Comment: 10 pages, no figure, some references and comments on gravitational perturbations are adde

The Asymptotic Dirichlet Problems on manifolds with unbounded negative curvature

Elton P. Hsu used probabilistic method to show that the asymptotic Dirichlet problem is uniquely solvable if the curvature satisfies the condition $-C e^{(2-\eta)r(x)} \leq K_M(x)\leq -1$ with $\eta\u3e0$. We give an analytical proof of the same statement. In addition, using this new approach we are able to establish two boundary Harnack inequalities under the curvature condition $-C e^{(2/3-\eta)r(x)} \leq K_M(x)\leq -1$ with $\eta\u3e0$. This implies that there is a natural homeomorphism between the Martin boundary and the geometric boundary of $M$. As far as we know, this is the first result of this kind under unbounded curvature conditions. Our proofs are modifications of arguments due to M. T. Anderson and R. Schoen

Development and characterisation of nano-multilayer CrAlSiN coating systems for cutting tools

Two types of CrAlSiN nano-multilayer coating were designed and synthesised on AISI M2 high speed steel. Selected coatings were also deposited on pre-nitrided M2 substrate to investigate the effect of duplex treatment. A series of type I CrAlSiN coatings, which have sharp interfaces between individual nano-layers, were designed with varying bilayer thickness. An fcc and an hcp phase were identified for all type I coatings, and it has been found that the bilayer thickness has a significant influence on the orientation of both phases, which in turn affects their mechanical properties. Type II CrAlSiN coatings, with blurred interfaces, were synthesised with a medium bilayer thickness. Due to the insignificant difference in composition between neighbouring nano-layers, only one fcc phase was found in type II CrAlSiN coating. The wear resistance of the new nano-multilayer CrAlSiN coating is about 10 times higher than CrN when tested at room and elevated temperatures. This could be attributed to high H/E ratio and good oxidation resistance conferred by the nano-multilayer structure and multi-component composition. It is also found that duplex treatment can improve the wear resistance of nano-multilayer coating by two orders of magnitude due to the improved load bearing capacity of the coating system