Let (M, g) be a classical Riemannian globally symmetric space of rank one and non-compact type. We prove the existence and uniqueness of solutions to the Dirichlet problem for harmonic maps into (M, g) with prescribed singularities along a closed submanifold of the domain. This generalizes our previous work where such maps into the hyperbolic plane were constructed. This problem, in the case wh...

It is known that there is no nonconstant bounded harmonic map from the Euclidean space R to the hyperbolic space H. This is a particular case of a result of S.-Y. Cheng. However, there are many polynomial growth harmonic maps from R to H by the results of Z. Han, L.-F. Tam, A. Treibergs and T. Wan. One of the purposes of this paper is to construct harmonic maps from R to H by prescribing bounda...

Let X be a complete noncompact Riemannian manifold with Ricci curvature and Sobolev radius (see §6 for the definition) bounded from below and Y a complete Riemannian manifold with nonpositive sectional curvature. We shall study some situations where a smooth map f : X → Y can be deformed continuously into a harmonic map, using a naturally defined flow. The flow used here is not the usual harmon...

We show that for a generic conformal metric perturbation of compact hyperbolic 3-manifold $\Sigma$ with Betti number $b_1$, the order vanishing Ruelle zeta function at zero equals $4-b_1$, while in case it is equal to $4-2b_1$. This contrast 2-dimensional where topological invariant. The proof uses microlocal approach dynamical functions, giving geometric description generalized Pollicott-Ruell...

We relate Gruet's formula for the heat kernel on real hyperbolic spaces to commonly used one derived from Millson induction and distinguishing parity of dimensions. The bridge between both formulas is settled by Yor's result joint distribution a Brownian motion its exponential functional at fixed time. This allows further with parameter Jacobi operator derive new integral representation Maass L...

the harmonic in distribution systems becomes an important problem due to an increase in nonlinear loads. this paper presents a new approach based on a graph algorithm for optimum placement of passive harmonic filters in a multi-bus system, which suffers from harmonic current sources. the objective of this paper is to minimize the network loss, the cost of the filter and the total harmonic disto...

We study the class of 1/|w|-harmonic K-quasiconformal mappings with angular ranges. After building a differential equation for the hyperbolic metric of an angular range, we obtain the sharp bounds of their hyperbolically partial derivatives, determined by the quasiconformal constant K. As an applicationwe get their hyperbolically bi-Lipschitz continuity and their sharp hyperbolically bi-Lipschi...

We study the topology of a complete asymptotically hyperbolic Einstein manifold such that its conformal boundary has positive Yamabe invariant. We proved that all maps from such manifold into any nonpositively curved manifold are homotopically trivial. Our proof is based on a Bochner type argument on harmonic maps.

We give results on the following questions about a topologically tame hyperbolic 3-manifold M : 1. Does M have nonzero square-integrable harmonic 1-forms? 2. Does zero lie in the spectrum of the Laplacian acting on Λ1(M)/Ker(d)?