Green's function and anti-holomorphic dynamics on a torus
arXiv:1507.01704 · doi:10.1090/proc/13044
Abstract
We give a new, simple proof of the fact recently discovered by C.-S. Lin and C.-L. Wang that the Green function of a torus has either three or five critical points, depending on the modulus of the torus. The proof uses anti-holomorphic dynamics. As a byproduct we find a one-parametric family of anti-holomorphic dynamical systems for which the parameter space consists only of hyperbolic components and analytic curves separating them.
17 pages, 3 figures (some details added, some overall revision)
Cited by in corpus (7)
- Schwarz reflections and the Tricorn
- An orthorhombic deformation family of Schwarz' H surfaces
- Moduli spaces for Lamé functions and Abelian integrals of the second kind
- Stacking disorder in periodic minimal surfaces
- On the number of solutions of some transcendental equations
- A note on the critical points of the localization landscape
- Antiholomorphic perturbations of Weierstrass Zeta functions and Green's function on tori