相关论文: Grafting, harmonic maps, and projective structures…
We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on…
A correspondence between different $Pin$-type structures on a compact surface and quadratic (linear) forms on its homology is constructed. Addition of structures is defined and expressed in terms of these quadratic forms.
We construct a parabolic entire minimal graph $S$ over a finite topology complete Riemannian surface $\Sigma$ of curvature $-1$ and infinite area (thus of non-parabolic conformal type). The vertical projection of this graph yields a…
The classical concept of affine locally symmetric spaces allows a generalization for various geometric structures on a smooth manifold. We remind the notion of symmetry for parabolic geometries and we summarize the known facts for…
A new concept of meromorphic $\Sigma$-factorization, for H\"{o}lder continuous functions defined on a contour $\Gamma$ that is the pullback of $\dot{\mathbb{R}}$ (or the unit circle) in a Riemann surface $\Sigma$ of genus 1, is introduced…
The systole of a hyperbolic surface is bounded by a logarithmic function of its genus. This bound is sharp, in that there exist sequences of surfaces with genera tending to infinity that attain logarithmically large systoles. These are…
The Gauss map of a given projective variety is the rational map that sends a smooth point to the tangent space at that point, considered as a point of the Grassmann variety. The present paper aims to generalize a result by H. Kaji on Gauss…
We are concerned with mapping class groups of surfaces with nonempty boundary. We present a very natural method, due to Thurston, of finding many different left orderings of such groups. The construction involves equipping the surface with…
In algebraic geometry, trigonal curves can always be embedded into Hirzebruch surfaces. In tropical geometry, the notion of trigonality does not have a unique translation. We focus on the characterization in terms of the existence of a…
We prove that a conformal mapping defined on the unit disk belongs to a weighted Bergman space if and only if certain integrals involving the harmonic measure converge. With the aid of this theorem, we give a geometric characterization of…
In earlier work, we constructed invariants of irreducible representations of the Kauffman skein algebra of a surface. We introduce here an inverse construction, which to a set of possible invariants associates an irreducible representation…
In this paper, we deal with the gluing of two surfaces, where the gluing locus is assumed to be a curve. We consider a moving frame along the gluing locus, and define developable surfaces with respect to the frame. Considering geometric…
We will investigate the local geometry of the surfaces in the $7$-dimensional Euclidean space associated to harmonic maps from a Riemann surface $\Sigma$ into $S^6$. By applying methods based on the use of harmonic sequences, we will…
We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of…
Following Thurston's geometrisation picture in dimension three, we study geometric manifolds in a more general setting in arbitrary dimensions, with respect to the following problems: (i) The existence of maps of non-zero degree (domination…
Riemann surfaces are two-dimensional manifolds with a conformal class of metrics. It is well known that the harmonic action functional and harmonic maps are tools to study the moduli space of Riemann surfaces. Super Riemann surfaces are an…
We consider the compactification M(atrix) theory on a Riemann surface Sigma of genus g>1. A natural generalization of the case of the torus leads to construct a projective unitary representation of pi_1(\Sigma), realized on the Hilbert…
Given a closed surface S of genus at least 2, we compare the symplectic structure of Taubes' moduli space of minimal hyperbolic germs with the Goldman symplectic structure on the character variety X(S, PSL(2,C)) and the affine cotangent…
Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In this survey, we give a generalization of geodesic laminations on surfaces endowed with a half-translation structure,…
Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…