Related papers: Penner coordinates for closed surfaces
We generalize the horofunction compactification to maps that are not distance functions. As an application we define a horofunction counterpart to the Teichm\"uller distance, and discuss its properties.
In this note, we highlight some properties of the metric projection onto a closed convex in a Hilbert space. In particular, we use some recent results on fixed points of nonexpansive potential operators.
A generalized version of the TKNN-equations computing Hall conductances for generalized Dirac-like Harper operators is derived. Geometrically these equations relate Chern numbers of suitable (dual) bundles naturally associated to spectral…
There are presented certain results on extending continuous linear operators defined on spaces of E-valued continuous functions (defined on a compact Hausdorff space X) to linear operators defined on spaces of E-valued measurable functions…
The basic arguments underlying the symplectic projector method are presented. By this method, local free coordinates on the constrait surface can be obtained for a broader class of constrained systems. Some interesting examples are…
Kashaev algebra associated to a surface is a noncommutative deformation of the algebra of rational functions of Kashaev coordinates. For two arbitrary complex numbers, there is a generalized Kashaev algebra. The relationship between the…
We discuss hypercomplex and hyperk\"ahler structures obtained from higher degree curves in complex spaces fibring over ${\mathbb{P}}^1$.
We prove that the pressure metric on the Teichm\"uller space of a bordered surface is incomplete and its partial completion can be given by the moduli space of metric graphs for a fat graph associated to the same bordered surface equipped…
We defined a new set of coordinates with respect to which the Thurston compactification of Teichmuller space is the radial compactification of Euclidean space.
We consider a geometric property of the closest-points projection to a geodesic in Teichm\"uller space: the projection is called contracting if arbitrarily large balls away from the geodesic project to sets of bounded diameter. (This…
We find necessary and sufficient conditions under which the complex coordinates on a flag manifold of a classical group described in [2] are Bochner coordinates.
There are several ways of a construction of a boundary of a symmetric space using pencils of geodesics: the Karpelevich boundary, the visibility boundary, the associahedral boundary, and the sea urchin. We give explicit descriptions of…
We discuss several geometric features of a Kummer surface associated with a (1,2)-polarized abelian surface defined over the field of complex numbers. In particular, we show that any such Kummer surface can be modeled as the double cover of…
This paper extends the decorated Teichm\"uller theory developed before for punctured surfaces to the setting of ``bordered'' surfaces, i.e., surfaces with boundary, and there is non-trivial new structure discovered. The main new result…
We show that the length function of a measured geodesic lamination is convex in Thurston's shear coordinates over Teichm\"uller space and strictly convex for generic laminations. We give some consequences of this result in the context of…
We enlarge the class of open Riemann surfaces known to be holomorphically embeddable into the plane by allowing them to have additional isolated punctures compared to the known embedding results.
The spherometer used for measuring radius of curvature of spherical surfaces is explicitly based on a geometric relation unique to circles and spheres. We present an alternate approach using coordinate geometry, which reproduces the…
The correspondence between 2-parameter families of oriented lines in ${\Bbb{R}}^3$ and surfaces in $T{\Bbb{P}}^1$ is studied, and the geometric properties of the lines are related to the complex geometry of the surface. Congruences…
Motivated by recent interest concerning "puncture repair" in the conformal geometry of compact Riemannian manifolds, a brief exposition on generalisation to the setting of quasiconformal mappings on certain metric measure spaces is…
Fermi coordinates are constructed as exact functions of the Schwar\-zschild coordinates around the world line of a static observer in the equatorial plane of the Schwarzschild spacetime modulo a single impact parameter determined implicitly…