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Green’s functions for quasi-hyperbolic metrics on degenerating Riemann surfaces with a separating node. (English) Zbl 0982.32013

Summary: We consider a family of compact Riemann surfaces of genus \(q\geq 2\) degenerating to a Riemann surface with a separating node and many non-separating nodes. We obtain the asymptotic behavior of Green’s functions associated to a continuous family of quasi-hyperbolic metrics on such degenerating Riemann surfaces.

MSC:

32G20 Period matrices, variation of Hodge structure; degenerations
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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