| Résume | A compact hyperbolic surface S of genus g is said to be extremal if it admits an extremal disc, a disc of the largest radius determined by g, where genus g is the number of handles if S is orientable (i.e. a Riemann surface); or the number of cross caps if S is non-orientable (i.e. a Klein surface). A natural question arising here is how many extremal discs are embedded in extremal surfaces. If S is orientable, we know the answer for every genus. In this talk we answer the question in the case that S is a non-orientable surface of genus 6, the final genus in our interest, and present all extremal surfaces admitting more than one extremal disc. The locus of every extremal disc is also obtained. Furthermore we determine the groups of automorphisms for these surfaces. |
