Search

A compact hyperbolic surface of genus g is called an extremal surface if it admits an extremal disc, a disc of the largest radius determined by g. Our problem is to find how many extremal discs are embedded in non-orientable extremal surfaces. It is known that non-orientable extremal surfaces of genus g > 6 contain exactly one extremal disc and that of genus 3 or 4 contain at most two. In the present paper we shall give all the non-orientable extremal surfaces of genus 5, and find the locations of all extremal discs in those surfaces. As a consequence, non-orientable extremal surfaces of genus 5 contain at most two extremal discs.

Let n > 1, m ≥ 1, g ≥ 3 and γ be given integers. The purpose of this paper is to determine the relations of n, m, g and γ for the existence of the symmetric Riemann surfaces S of type (n, m) with genus g and species γ. If n is an odd prime, the relations are known in [3]. In the case that n is odd, we shall show the analogous result when E(S) is isomorphic to a cyclic group Z2n and when the quotient space S/E(S) is orientable.

Search Results

Refine search

Refine search

Actions for selected content:

2 results

COMPACT NON-ORIENTABLE SURFACES OF GENUS 5 WITH EXTREMAL METRIC DISCS

The existence of symmetric Riemann surfaces determined by cyclic groups

Search Results

Refine search

Refine search

Actions for selected content:

Save Search

2 results

COMPACT NON-ORIENTABLE SURFACES OF GENUS 5 WITH EXTREMAL METRIC DISCS

The existence of symmetric Riemann surfaces determined by cyclic groups