Complex Analysis and Surface Theory II
Prerequisiti
Prerequisites al consist mainly of the material covered in first-year courses and in the first part of this course. It is possible that some results proved in second-year courses may be used
Programma
Dirichlet problem
Classification of complex tori
Liouville's theorem for conformal maps
Hopf's theorem for surfaces with constant mean curvature
Obiettivi formativi
The purpose of the course is to present elements of complex analysis, and in particular the conformal theory of holomorphic functions. This will be used in the study of the structure of surfaces in three-dimensional Euclidean space. This will help characterize some relevant classes of surfaces, such as minimal or constant mean curvature surfaces.
Riferimenti bibliografici
Useful references will be classical books on Complex Analysis, such as those by Ahlfors and Gamelin, and some concerning minimal surfaces, such as those by Osserman and Fomenko-Tuzhilin. For surface geometry, classic texts are Do Carmo's and some of Spivak's volumes.