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Proper affine actions and geodesic flows of hyperbolic surfaces
hyperbolic surfaces geodesic fl ows
2015/9/29
Let €0 O.2; 1/ be a Schottky group, and let † D H
2=€0 be the corresponding
hyperbolic surface. Let C.†/ denote the space of unit length geodesic currents
on †. The cohom...
In the study of the geometry of curves on surfaces, the following
question often arises: given a one-parameter family of divisors over a pointed
curve, what does the central ber look like after sta...
Doubling and Desingularization Constructions for Minimal Surfaces
Differential geometry minimal surfaces partial differential equations
2011/2/28
In the first part of the paper we discuss the current status of the application of the gluing methodology to doubling and desingularization constructions for minimal surfaces in Riemannian three-manif...
Log del Pezzo Surfaces of Rank 2 and Cartier Index 3 with a Unique Singularity
Log del Pezzo surfaces Quotient singularities
2011/1/18
Log del Pezzo surfaces play the role of the opposite of surfaces of general type. We will completely classify all the log del Pezzo surfaces of rank 2 and Cartier index 3 with a unique singularity.
The double cover of cubic surfaces branched along their Hessian
double cover cubic surfaces branched
2011/2/23
We prove the relation between the Hodge structure of the double cover of a nonsingular cubic surface branched along its Hessian and the Hodge structure of the triple cover of P3 branched along the cub...
Flippable tilings of constant curvature surfaces
Flippable tilings constant curvature surfaces
2011/1/19
We call “flippable tilings” of a constant curvature surface a tiling by “black” and “white” faces, so that each edge is adjacent to two black and two white faces (one of each on each side), the black ...
We show that projective K3 surfaces with odd Picard rank contain infinitely many rational curves. Our proof extends the Bogomolov-Hassett-Tschinkel approach, i.e., uses moduli spaces of stable maps an...
Counting Essential Surfaces in a Closed Hyperbolic 3-Manifold
Counting Essential Surfaces Closed Hyperbolic 3-Manifold
2011/1/21
Let M3 be a closed hyperbolic three manifold. We show that the number of genus g surface subgroups of 1(M3) grows like g 2g.
Growth of Weil-Petersson volumes and random hyperbolic surfaces of large genus
Growth of Weil-Petersson volumes random hyperbolic surfaces of large genus
2011/1/20
In this paper, we investigate the geometric properties of hyperbolic surfaces by studying the lengths of simple closed geodesics. The moduli space Mg,n of complete hyperbolic surfaces of genus g ≥ 2 w...
In this paper, we extend the study of local scales of a function [JL09] to studying local scales on curves and surfaces. In the case of a function f, the local scales of f at x is computed by measurin...
Algorithms for Del Pezzo Surfaces of Degree 5 (Construction, Parametrization)
Algorithms Del Pezzo Surfaces of Degree 5
2010/12/9
It is well known that every Del Pezzo surface of degree 5 defined over k is parametrizable over k. In this paper we give an efficient construction for parametrizing, as well as algorithms for construc...
For any m > 1, we construct properly embedded minimal surfaces in H2 R with genus zero,
infinitely many vertical planar ends and m limit ends. We also provide examples with an infinite countable nu...
Circle Decompositions of Surfaces
Topological surfaces circle partitions Jordan-Sch¨onflies Theorem upper semicontinuous decompositions
2010/11/29
We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic
zero, and w...
On the Local Isometric Embedding in R^3 of Surfaces with Gaussian Curvature of Mixed Sign
Local Isometric Embedding R^3 of Surfaces Gaussian Curvature of Mixed Sign
2010/12/15
We study the old problem of isometrically embedding a 2-dimensional Rie-mannian manifold into Euclidean 3-space. It is shown that if the Gaussian curvature vanishes to finite order and its zero set co...
Rigidity of Frameworks Supported on Surfaces
bar-joint framework framework on a surface rigid framework
2010/12/9
A theorem of Laman gives a combinatorial character-isation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in R2. A more general theory is devel-oped for framew...