2016/11/29 by Baryshnikov, Yuliy, Shapiro, Boris
#30F30 (Primary) #31A05 (Secondary) #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1611.09494
In this paper, motivated by the classical notion of a Strebel qua- dratic differential on a compact Riemann surface without boundary, we in- troduce several classes of quadratic differentials (called non-chaotic, gradient, and positive gradient) which possess some properties of Strebel differentials and appear in applications. We discuss the relation between gradient differen- tials and special signed measures supported on their set of critical trajectories. We provide a characterisation of gradient differentials for which there exists a positive measure in the latter class.