Complex Analysis and Surface Theory I

Period of duration of course
‌‌
Course info
Number of course hours
60
Number of hours of lecturers of reference
60
CFU 9
‌‌

Modalità esame

Written and oral exams

Note modalità di esame

Written and oral exams, exercises during class

Lecturer

View lecturer details

Lecturer

Gian Maria Dall'Ara

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

- Holomorphic functions and study of isolated singularities 


- Elements of Riemann surfaces, automorphisms of disc, plane, sphere


- Differential forms and integration 


- Geometry of surfaces in Euclidean space 


- Isothermal coordinates 


- Enneper-Weierstrass representation 


- Bernstein's theorem 


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 books concerning minimal surfaces, such as those by Osserman and Fomenko-Tuzhilin. For surface geometry classic texts are that of Do Carmo and some of Spivak's volumes.