Szego Kernel Asymptotics for High Power of CR Line Bundles and Kodaira Embedding Theorems on CR Manifolds

ISBN-13: 9781470441012 / Angielski / Miękka / 2018 / 140 str.

Chin-Yu Hsiao; Dylan P. Thurston

Opis

Let $X$ be an abstract not necessarily compact orientable CR manifold of dimension $2n-1$, $ngeqslant 2$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Given $qin {0,1,ldots,n-1}$, let $Box ^{(q)}_{b,k}$ be the Gaffney extension of Kohn Laplacian for $(0,q)$ forms with values in $L^k$.

Spis treści

• Introduction and statement of the main results;
• More properties of the phase $\varphi (x,y,s)$; Preliminaries;
• Semi-classical $\Box ^{(q)}_{b,k}$ and the characteristic manifold for $\Box ^{(q)}_{b,k}$;
• The heat equation for the local operatot $\Box ^{(q)}_s$;
• Semi-classical Hodge decomposition theorems for $\Box ^{(q)}_{s,k}$ in some non-degenerate part of $\Sigma $; Szego kernel asymptotics for lower energy forms;
• Almost Kodaira embedding Theorems on CR manifolds;
• Asymptotic expansion of the Szego kernel;
• Szego kernel asymptotics and Kodairan embedding Theorems on CR manifolds with transversal CR $S^1$ actions;
• Szego kernel asymptotics on some non-compact CR manifolds;
• The proof of Theorem 5.28;
• References.