PhD course
Real submanifolds of complex space
Lecturer: Egmont Porten (Mid Sweden University)

25 January - 15 February 2018


Schedule:

1. Thursday January 25 
2. Tuesday January 30
3. Wednesday January 31
4. Thursday February 1
5. Tuesday February 6
6. Thursday February 8
7. Tuesday February 13
8. Thursday February 15
 
All lectures will be held in Aula D'Antoni from 14:00 to 16:00


The course addresses advanced students, PhD students and researcher.

Program

Lecture 1: General introduction, first examples and problems.
Lecture 2: Boundary values of holomorphic functions, CR-functions, removable singularities, of CR-functions: relation of the topic to polynomial convexity and envelopes of holomorphy.
Lecture 3: Surfaces in C², filling of 2-spheres, characteristic foliations, application to removable singularity in strictly pseudoconvex and general boundaries in C².
Lecture 4: More envelopes of holomorphy, example of a 2-sphere bounding two Levi flat 3-balls.
Lecture 5: General CR-manifolds, holomorphic discs and the Bishop equation, Levi curvature and extension of CR-functions, propagation along CR orbits, simplified proof of holomorphic wedge extension from minimal CR manifolds.
Lecture 6: L2-methods on Riemann domains, functions with polynomial growth towards the boundary, Dloussky’s theorem on subvarities that are singular loci.
Lecture 7: Pseudoconcave CR manifolds, problems on regularity and extension, subelliptic estimates for tangential CR equations, essential pseudoconcave manifolds.
Lecture 8: Local holomorphic extension to full neighbourhoods, relation to hypoellipticity, homogenous examples, microlocal view and open problems.

This course is funded by a INdAM Visiting Scholarship