On the Dirichlet and the Riemann-Hilbert Problem on Möbius Strips

Abstract

In this paper we give 1) a description of harmonic functions on Möbius strips as a manifold modelled on a subspace of the (Sobolev) space of holomorphic functions on ring domains, 2) a functional-analytic theory for the Laplacian, e.g., the Dirichlet boundary value problem and 3) the Fredholm theory for the Riemann-Hubert operator.