Related papers: Hyperbolic metrics, homogeneous holomorphic functi…

A classical result of Sampson and Schoen-Yau in 1978 states that every diffeomorphism between compact hyperbolic Riemann surfaces is homotopic to an harmonic diffeomorphism. As conjectured by Schoen in 1993 and partially proved by Wan in…

We consider certain inequalities among the Apollonian metric, the Apollonian inner metric, the $j$ metric and the quasihyperbolic metric. We verify that whether these inequalities can occur in simply connected planar domains and in proper…

We consider asymptotically hyperbolic manifolds whose metrics have Sobolev-class regularity, and introduce several technical tools for studying PDEs on such manifolds. Our results employ two novel families of function spaces suitable for…

In this article we make an explicit approach to the higher degree case of the problem: " For a given $CM$ field $M$, construct its maximal abelian extension $C(M)$ (i.e. the Hilbert class field) by the adjunction of special values of…

For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic…

Based on a well known Sh.-T. Yau theorem we obtain that the real part of a holomorphic function on a K\"{a}hler manifold with the Ricci curvature bounded from below by $-1$ is contractive with respect to the distance on the manifold and the…

The function on the Teichmueller space of complete, orientable, finite-area hyperbolic surfaces of a fixed topological type that assigns to a hyperbolic surface its maximal injectivity radius has no local maxima that are not global maxima.

Invariants for Riemann surfaces covered by the disc and for hyperbolic manifolds in general involving minimizing the measure of the image over the homotopy and homology classes of closed curves and maps of the $k$-sphere into the manifold…

We prove sharp bounds for the product and the sum of two hyperbolic distances between the opposite sides of hyperbolic Lambert quadrilaterals in the unit disk. Furthermore, we study the images of Lambert quadrilaterals under quasiconformal…

We consider the dynamics of semi-hyperbolic semigroups generated by finitely many rational maps on the Riemann sphere. Assuming that the nice open set condition holds it is proved that there exists a geometric measure on the Julia set with…

We discuss hypersurface motions in Riemannian manifolds whose normal velocity is a function of the induced hypersurface volume element and derive a second order partial differential equation for the corresponding time function $\tau(x)$ at…

We introduce a natural equivalence relation on the space $\sH_0$ of horofunctions of a word hyperbolic group that take the value 0 at the identity. We show that there are only finitely many ergodic measures that are invariant under this…

The Grothendieck conjecture for hyperbolic curves over finite fields was solved affirmatively by Tamagawa and Mochizuki. On the other hand, (a ``weak version'' of) the Grothendieck conjecture for some hyperbolic curves over algebraic…

Let $G$ denote an infinite-dimensional Heisenberg-like group, which is a class of infinite-dimensional step 2 stratified Lie groups. We consider holomorphic functions on $G$ that are square integrable with respect to a heat kernel measure…

On generalized Heisenberg-type groups $\mathbb{G}(2n,m,\mathbb{U},\mathbb{W})$, we give uniform volume estimates for the ball defined by a large class of Carnot-Carath\'{e}odory distances, and establish weak (1, 1) $O(C^m \, n)$-estimates…

We prove the hyperbolicity of ergodic maximal entropy measures for a class of partially hyperbolic diffeomorphisms of $\mathbb{T}^{d}$, which have a compact two-dimensional center foliation.

The N-dimensional Hamiltonian H formed by a curved kinetic term (depending on a function f), a central potential (depending on a function U), a Dirac monopole term, and N centrifugal terms is shown to be quasi-maximally superintegrable for…

We obtain so far unproved properties of a ratio involving a class of Hermite and parabolic cylinder functions. Those ratios are shown to be strictly decreasing and bounded by universal constants. Differently to usual analytic approaches, we…

Let $f$ be a nonzero holomorphic function in the unit ball $\mathbb B$ of the $n$-dimensional complex Euclidean space $\mathbb C^n$ such that the function $f$ vanishes on the set ${\sf Z}\subset \mathbb B$ and satisfies the constraint…

A Teichm\"uller space $Teich$ is a quotient of the space of all complex structures on a given manifold $M$ by the connected components of the group of diffeomorphisms. The mapping class group $\Gamma$ of $M$ is the group of connected…