To learn some techniques to deal with some geometric problems in the spaces of several complex variables
Prerequisites
Elementary notions of one complex variable, geometry and linear algebra
Teaching Methods
Frontal lessons
Type of Assessment
oral exam
Course program
Program of the course Geometrical methods
Cap.1
Complex functions; Cauchy theorem; zeros of a holomorphic function; open mapping theorem; maximum's principle;Schwarz lemma.
Cap.2
Riemann mapping theorem
Cap 3
The automorphisms group of the disc; Montel's theorem
Cap. 4
Characterization of the disc via the automorphisms group; scaling method in one dimension.
Cap.5
Complex space of more than one dimension. Cartan's theorem and some consequences. Circular domains. The automorphisms group of the ball.
Cap.6
The automorphisms group of the polydisc. Open mapping theorem in C^n
Cap.7
Cartan-Caratheodory-Kaup theorem
Cap.8
Kobayashi and Caratheodory volums. Wong- Rosay theorem