Compact Non-orientable Surfaces of Genus 6 with Extremal Metric Discs
نویسندگان
چکیده
A compact hyperbolic surface of genus g is said to be extremal if it admits an extremal disc, a disc of the largest radius determined only by g. We discuss how many extremal discs are embedded in non-orientable extremal surfaces of genus 6. This is the final genus in our interest because it is already known for g = 3, 4, 5, or g > 6. We show that non-orientable extremal surfaces of genus 6 admit at most two extremal discs. The locus of extremal discs is also obtained for each surface. Consequently non-orientable extremal surfaces of arbitrary genus g 3 admit at most two extremal discs. Furthermore we determine the groups of automorphisms of non-orientable extremal surfaces of genus 6 with two extremal discs.
منابع مشابه
Compact Non-orientable Hyperbolic Surfaces with an Extremal Metric Disc
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