Positive holomorphic differentials on Klein surfaces

Newcomb Greenleaf and Walter Read

Vol. 32 (1970), No. 3, 711–713

DOI: 10.2140/pjm.1970.32.711

Abstract

Let X be a compact Klein surface with boundary ∂X, and let β be an orientation of ∂X. We conjecture that there is a holomorphic differential which is positive on p if and only if 8 is not induced by an orientation of X, and we prove this when χ is elliptic or hyperelliptic.

Mathematical Subject Classification

Primary: 30.45

Secondary: 14.00

Milestones

Received: 5 August 1969

Published: 1 March 1970