Extremal length and Dirichlet problem on Klein surfaces

Abstract

The object of this paper is to extend the method of extremal length to Klein surfaces by solving conformally invariant extremal problems on the complex double. Within this method we define the extremal length, the extremal distance, the conjugate extremal distance, the modulus, the reduced extremal distance on a Klein surface and we study their dependences on arcs.

Keywords

• klein surface
• extremal length
• extremal distance