Sums of squares in pseudoconvex hypersurfaces and torsion phenomena for Catlin's boundary systems
Abstract
Given a pseudoconvex hypersurface in C^n and an arbitrary weight, we show the existence of local coordinates in which the polynomial model contains a particularly simple sum of squares of monomials. Our second main result provides a normalization of a part of any Catlin boundary system. We illustrate by an example that this normalization cannot be extended to the rest of the boundary system due to the existence of what we refer to as torsion.
 Publication:

arXiv eprints
 Pub Date:
 June 2018
 arXiv:
 arXiv:1806.01359
 Bibcode:
 2018arXiv180601359B
 Keywords:

 Mathematics  Complex Variables;
 32T27;
 41A10 (Primary) 32F17 (Secondary)
 EPrint:
 22 pages