arXiv subjects
Publications and source records attributed to Kunio Obitsu.
We give some estimates for the asymptotic orders of degenerating Eisenstein series for some families of degenerating punctured Riemann surfaces, which is motivated by the question identifying $L_{2}$-cohomology of the Takhtajan-Zograf metric that is originally asked by To and Weng.
The family hyperbolic metric for the plumbing variety $\{zw=t\}$ and the non holomorphic Eisenstein series $E(ΞΆ;2)$ are combined to provide an explicit expansion for the hyperbolic metrics for degenerating families of Riemann surfaces. Applications include an asymptotic expansion for the Weil-Petersson metric and a local form of symplectic reduction.