To, Wing-Keung; Weng, Lin Green’s functions for quasi-hyperbolic metrics on degenerating Riemann surfaces with a separating node. (English) Zbl 0982.32013 Ann. Global Anal. Geom. 17, No. 3, 239-265 (1999). 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 Keywords:degenerating Riemann surfaces; Green’s functions; quasi-hyperbolic metrics PDFBibTeX XMLCite \textit{W.-K. To} and \textit{L. Weng}, Ann. Global Anal. Geom. 17, No. 3, 239--265 (1999; Zbl 0982.32013) Full Text: DOI