Elizabethan vortices

Abstract

Radial solutions to the elliptic sinh-Gordon and Tzitzeica equations can be interpreted as Abelian vortices on certain surfaces of revolution. These surfaces have a conical excess angle at infinity (in a way which makes them similar to Elizabethan ruff collars). While they can not be embedded in the Euclidean 3-space, we will show that they can be globally embedded in the hyperbolic space. The existence of these hyperbolic embeddings follows from the asymptotic analysis of a Painleve III ODE.

Dedicated to Nick Manton on the occasion of his 70th birthday. Some typos from the journal version corrected

References in corpus (5)

• Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painleve' Equation: II
• Five Vortex Equations
• Nineteen vortex equations and integrability
• The Kijowski--Liu--Yau quasi-local mass of the Kerr black hole horizon
• Cartan Connections and Integrable Vortex Equations

Cited by in corpus (1)

• Separation of Variables and Superintegrability on Riemannian Coverings