The Einstein/Abelian-Yang-Mills Equations reduce in the stationary and axially symmetric case to a harmonic map with prescribed singularities φ : R \Σ → H C into the (k+1)-dimensional complex hyperbolic space. In this paper, we prove the existence and uniqueness of harmonic maps with prescribed singularities φ : R \ Σ → H, where Σ is an unbounded smooth closed submanifold of R of codimension at...

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One of the most famous results Dedekind is transformation law $$\log \Delta (z)$$ . After a half-century, Rademacher modified Dedekind’s result and introduced an $${{\,\textrm{SL}\,}}_2({\mathbb {Z}})$$ -conjugacy class invariant (integer-valued) function $$\Psi (\gamma )$$ called symbol. Inspired by Ghys’ work on modular knots, Duke–Imamo?lu–Tóth (2017) constructed hyperbolic analogue In this ...