Real submanifolds of
Lecturer: Egmont Porten (Mid Sweden
25 January - 15 February 2018
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
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
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