Harmonic measures and Poisson kernels on Klein surfaces

Abstract

We introduce harmonic measure on a Klein surface and obtain a formula for the solution of the Dirichlet problem on a Klein surface, which is an analogue for the Poisson integral. We rewrite the Radon-Nikodym derivative of harmonic measure against the corresponding arc length.

Keywords

• Klein surface
• Green's function
• harmonic measure
• Poisson kernel