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arXiv · 2606.24907

The Fefferman-Szeg\H{o} Sphericity Criterion in Complex Dimension Three

Venkata Siddharth Pendyala
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Abstract

We establish a Fefferman-Szeg\H{o} characterization of local CR sphericity for smoothly bounded strongly pseudoconvex domains in complex dimension three. We derive the boundary expansion of the normalized determinant of the Fefferman-Szeg\H{o} metric and prove that its second-order coefficient is a universal multiple of the squared Chern-Moser curvature. Hence, vanishing of the second-order deviation from the ball model is equivalent to local sphericity. A logarithmic stability theorem for the associated Monge-Amp\`ere determinant controls the remainder and completes the dimension-three case.

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Venkata Siddharth Pendyala. 2026-06-16. The Fefferman-Szeg\H{o} Sphericity Criterion in Complex Dimension Three. https://arxiv.org/abs/2606.24907

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