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OverviewLet $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $n\geqslant 2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given $q\in \{0,1,\ldots ,n-1\}$, let $\Box ^{(q)}_{b,k}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$ forms with values in $L^k$. For $\lambda \geq 0$, let $\Pi ^{(q)}_{k,\leq \lambda} :=E((-\infty ,\lambda ])$, where $E$ denotes the spectral measure of $\Box ^{(q)}_{b,k}$. In this work, the author proves that $\Pi ^{(q)}_{k,\leq k^{-N_0}}F^*_k$, $F_k\Pi ^{(q)}_{k,\leq k^{-N_0}}F^*_k$, $N_0\geq 1$, admit asymptotic expansions with respect to $k$ on the non-degenerate part of the characteristic manifold of $\Box ^{(q)}_{b,k}$, where $F_k$ is some kind of microlocal cut-off function. Moreover, we show that $F_k\Pi ^{(q)}_{k,\leq 0}F^*_k$ admits a full asymptotic expansion with respect to $k$ if $\Box ^{(q)}_{b,k}$ has small spectral gap property with respect to $F_k$ and $\Pi^{(q)}_{k,\leq 0}$ is $k$-negligible away the diagonal with respect to $F_k$. By using these asymptotics, the authors establish almost Kodaira embedding theorems on CR manifolds and Kodaira embedding theorems on CR manifolds with transversal CR $S^1$ action. Full Product DetailsAuthor: Chin-Yu Hsiao , Dylan P. ThurstonPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.242kg ISBN: 9781470441012ISBN 10: 1470441012 Pages: 140 Publication Date: 30 August 2018 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |