| Résume | In this sequel to our work on moduli space of hybrid curves, we define a hybrid notion of Laplacian, formulate a hybrid Poisson equation, and give a mathematical meaning to the question of the convergence both of the Laplace operator and the solutions to the Poisson equation on Riemann surfaces. As an application, we formulate a hybrid notion of Green function and use this to obtain a layered description of the asymptotics of Arakelov Green functions on Riemann surfaces close to the boundary of their moduli spaces. This solves a well-studied problem arising from the Arakelov geometry of Riemann surfaces. Based on joint works with Noema Nicolussi. |
