Topological Loewner theory on Riemann surfaces

Abelian Gauge Theory on Riemann Surfaces and New Topological Invariants

Ideal Theory on Open Riemann Surfaces

Introduction. The theorems of the classical ideal theory in fields of algebraic numbers hold in rings of analytic functions on compact Riemann surfaces. The surfaces admitted in our discussion are closely related to algebraic surfaces; we deal either with compact surfaces from which a finite number of points are omitted or, more generally, with surfaces determined by an algebroid function. The ...

Abelian Gauge Theory on Riemann Surfaces

An Abelian gauge eld theory framed on a complex line bundle L over a compact Riemann surface M is developed which allows the coexistence, simultaneously in the same model, of magnetic vortices and antivortices represented by the N zeros and P poles of a section of L. The quantized minimum energy E is given in terms of the rst Chern class c 1 (L) and by a certain intersection number obtained fro...

Topological Classification of Conformal Actions on pq-Hyperelliptic Riemann Surfaces

A compact Riemann surface X of genus g > 1 is said to be p-hyperelliptic if X admits a conformal involution ρ for which X/ρ is an orbifold of genus p. Here we classify conformal actions on 2-hyperelliptic Rieman surfaces of genus g > 9, up to topological conjugacy and determine which of them can be maximal.

Hyperelliptic Surfaces Are Loewner

We prove that C. Loewner’s inequality for the torus is satisfied by conformal metrics on hyperelliptic surfaces X , as well. In genus 2, we first construct the Loewner loops on the (mildly singular) companion tori, locally isometric to X away from Weierstrass points. The loops are then transplanted to X , and surgered to obtain a Loewner loop on X . In higher genus, we exploit M. Gromov’s area ...