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arXiv · 1610.04669

Szeg\H{o} kernel asymptotic expansion on CR manifolds with $S^1$ action

Hendrik Herrmann·Chin-Yu Hsiao·Xiaoshan Li
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Abstract

Let $X$ be a compact connected strongly pseudoconvex CR manifold of dimension $2n+1, n \ge 1$ with a transversal CR $S^1$ action on $X$. We establish an asymptotic expansion for the $m$-th Fourier component of the Szeg\H{o} kernel function as $m\rightarrow\infty$, where the expansion involves a contribution in terms of a distance function from lower dimensional strata of the $S^1$ action. We also obtain explicit formulas for the first three coefficients of the expansion.

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Hendrik Herrmann, Chin-Yu Hsiao, Xiaoshan Li. 2016-10-14. Szeg\H{o} kernel asymptotic expansion on CR manifolds with $S^1$ action. https://doi.org/10.1142/s0129167x18500611

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