On the HJY Gap Conjecture in CR geometry vs. the SOS Conjecture for polynomials

2015/08/18 by Peter Ebenfelt, Ebenfelt, Peter · 4 citations
Mathematics · #Holomorphic and Operator Theory #Advanced Banach Space Theory #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.1508.04205

Abstract

We show that the Huang-Ji-Yin (HJY) Gap Conjecture concerning CR mappings between spheres follows from a conjecture regarding Sums of Squares (SOS) of polynomials. The connection between the two problems is made by the CR Gauss equation and the fact that the former conjecture follows from the latter follows from a recent result, due to the author, on partial rigidity of CR mappings of strictly pseudoconvex hypersurfaces into spheres.

Cited by

• Some results related to Macaulay's Theorem about Hilbert functions and applications
• A Newton-Okounkov Body Viewpoint on the SOS Conjecture
• Group-Invariant CR maps of the sphere \mathbbS⁵
• Macaulay representation of the prolongation matrix and the SOS conjecture

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