Asymptotics of torus equivariant Szegö kernel on a compact CR manifold
by Wei-Chuan Shen  

Vol. 14 No. 3 (2019) P.331~P.383

DOI:	https://doi.org/10.21915/BIMAS.2019303
	10.21915/BIMAS.2019303

ABSTRACT

For a compact CR manifold $(X,T^{1,0}X)$ of dimension $2n+1$, $n\geq 2$, admitting a $S^1\times T^d$ action, if the lattice point $(-p_1,\cdots,-p_d)\in\mathbb{Z}^{d}$ is a regular value of the associate CR moment map $\mu$, then we establish the asymptotic expansion of the torus equivariant Szego kernel $\Pi^{(0)}_{m,mp_1,\cdots,mp_d}(x,y)$ as $m\to +\infty$ under certain assumptions of the positivity of Levi form and the torus action on $Y:=\mu^{-1}(-p_1,\cdots,-p_d)$.

KEYWORDS
Equivariant Szegö kernel asymptotics, Analysis on CR manifolds

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 2000 Mathematics Subject Classification. Primary: 32V20 ; Secondary: 35S30, 58J40

MILESTONES

Received: 2018-10-15
Revised :
Accepted:

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