Explicit formulas for Green's functions on the annulus and on the Möbius strip

Abstract

Given a fixed point free antianalytic involution k of a domain G in thecomplex plane, bounded by a finite number of analytic curves, k-invariant Green’sfunctions are defined on G. The Lindelof’s principle is extended to k-invariantGreen’s functions. When G is the annulus, k-invariant Green’s functions areobtained in the explicit form. Since the factorization of the annulus by the group 〈k〉generated by k produces a Mobius strip, the respective result helped us to obtain explicitforms for Green’s functions on the Mobius strip.