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REFLECTION PRINCIPLE IN HIGHER DIMENSION SERGEY PINCHUK
 

Summary: REFLECTION PRINCIPLE IN HIGHER DIMENSION
SERGEY PINCHUK
Department of Mathematics, Indiana University,
Bloomington, IN 47401 (USA), e-mail pinchuk@indiana.edu
Notes written by Alberto Saracco
Scuola Normale Superiore, Piazza dei Cavalieri, 7
56126 Pisa, Italy, e-mail a.saracco@sns.it
Abstract. These are the notes of a course given by Prof. Sergey Pinchuk in July 2005 at the
summer school on "Real PDE's for Complex and CR-Geometry" held at ITC-IRST in Povo -
Trento.
The focus is on the reflection (Schwarz) principle in Cn
, n 2, and on results of extension
of holomorphic and CR-functions that can be obtained applying it. The notes contain only the
main ideas underlying the results. For complete proofs we refer to [6].
Contents
1. Introduction 2
2. Reflection principle in C 2
3. Reflection principle and extension theorems in Cn, n > 1 3
3.1. Edge of the Wedge Theorem 4
3.2. Extension in the strictly pseudoconvex case 5

  

Source: Abbondandolo, Alberto - Scuola Normale Superiore of Pisa

 

Collections: Mathematics