Related papers: Plumbing coordinates on Teichmueller space: a coun…

Expected duality and approximation properties are shown to fail on Bergman spaces of domains in $\mathbb{C}^n$, via examples. When the domain admits an operator satisfying certain mapping properties, positive duality and approximation…

In this work we describe a class of subsets of the Euclidean plane which, with the induced length metric, are locally $CAT(0)$ spaces and we show that the gluing of two such subsets along a piece of their boundary is again a locally…

Let S be a nonexceptional oriented surface of finite type. We construct an uncountable family of probability measures on the space of area on holomorphic quadratic differentials over the moduli space for S containing the usual Lebesgue…

We compare two families of left-invariant metrics on a surface group $\Gamma=\pi_1(\Sigma)$ in the context of course-geometry. One family comes from Riemannian metrics of negative curvature on the the surface $\Sigma$, and another from…

The twistor construction is applied for obtaining examples of generalized complex structures (in the sense of N. Hitchin) that are not induced by a complex or a symplectic structure.

We introduce the concept of a new kind of symmetric homeomorphisms on the unit circle, which is derived from the generalization of symmetric homeomorphisms on the real line. By the investigation of the barycentric extension for this class…

Using the Maskit coordinates for Teichmuller space, we prove the existence of new families of one dimensional subspaces on which the Caratheodory and Kobayashi metrics agree.

For any analytically finite Riemann surface, the Teichm\"uller modular group is countable, but it is not easy to find an analytically infinite Riemann surface for which the Teichm\"uller modular group is countable. In this paper, we show…

We prove that the Teichmuller Space of Riemann Surfaces of genus g>1, equipped with the Teichmuller metric, is not a Gromov Hyperbolic space.

Many quantum groups and quantum spaces of interest can be obtained by cochain (but not cocycle) twist from their corresponding classical object. This failure of the cocycle condition implies a hidden nonassociativity in the noncommutative…

In this paper we give a short geometric proof of a generalization of a well-known result about reduction of codimension for submanifolds of Riemannian symmetric spaces.

The problem of starlikeness of Teichmuller spaces in Bers' embedding was raised in 1974 and is solved (negatively) for Teichmuller spaces of sufficiently large dimensions. The original proof given by the author relies on the existence of…

There are many tools for studying local dynamics. An important problem is how this information can be used to obtain global information. We present examples for which local stability does not carry on globally. To this purpose we construct,…

If one could assume that local coordinates in a Riemannian manifold were orthogonal, then local expressions for differential operators, and curvature computations, would be simplified. It is always possible on 2-manifolds, using geometric…

The present paper is exclusively devoted to counterexamples about commutators and self commutators of unbounded operators on a Hilbert space. As a bonus, we provide a simpler counterexample than McIntosh's famous example obtained some while…

We show that any grafting ray in Teichm\"{u}ller space is (strongly) asymptotic to some Teichm\"{u}ller geodesic ray. As an intermediate step we introduce surfaces that arise as limits of these degenerating Riemann surfaces. Given a…

We construct new coordinates for the Teichm\"uller space Teich of a punctured torus into $\bold{R} \times\bold{R}^+$. The coordinates depend on the representation of Teich as a space of marked Kleinian groups $G_\mu$ that depend…

We prove that locally conformally K\"ahler metrics on certain compact complex surfaces with odd first Betti number can be deformed to new examples of bi-Hermitian metrics.

It is shown that the tessellation of a compact, negatively curved surface induced by a typical long geodesic segment, when properly scaled, looks locally like a Poisson line process. This implies that the global statistics of the…

A basic assumption of tiling theory is that adjacent tiles can meet in only a finite number of ways, up to rigid motions. However, there are many interesting tiling spaces that do not have this property. They have "fault lines", along which…