Complex Analysis and Surface Theory I
Prerequisiti
Prerequisites al consist mainly of the material covered in first-year courses. It is possible that some results proved in second-year courses may be used
Programma
- Numeri complessi - Funzioni olomorfe e loro proprieta' principali - Superfici di Riemann, e tempo permettendo elementi di teoria di Teichmuller - Forme differenziali - Geometria delle superfici nello spazio Euclideo - Coordinate isoterme - Rappresentazione di Weierstrass - Teoremi di Bernstein e Hopf per superfici minime e a curvatura media costante
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 classic books on Complex Analysis, such as those by Ahlfors and Gamelin, and some on minimal surfaces, such as those by Osserman and Fomenko-Tuzhilin. For surface geometry, classic texts include Do Carmo's and some of Spivak's volumes.