Szegő kernel asymptotics for high power of CR line bundles and Kodaira embedding theorems on CR manifolds
Let 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...
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| Format: | E-Book Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
2018
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| Ausgabe: | 1 |
| Schriftenreihe: | Memoirs of the American Mathematical Society |
| Schlagworte: | |
| ISBN: | 9781470441012, 1470441012 |
| ISSN: | 0065-9266, 1947-6221 |
| Online-Zugang: | Volltext |
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- Introduction and statement of the main results -- More properties of the phase <inline-formula content-type="math/mathml"> φ ( x , y , s ) \varphi (x,y,s) </inline-formula> -- Preliminaries -- Semi-classical <inline-formula content-type="math/mathml"> ◻ b , k ( q ) \Box ^{(q)}_{b,k} </inline-formula> and the characteristic manifold for <inline-formula content-type="math/mathml"> ◻ b , k ( q ) \Box ^{(q)}_{b,k} </inline-formula> -- The heat equation for the local operatot <inline-formula content-type="math/mathml"> ◻ s ( q ) \Box ^{(q)}_s </inline-formula> -- Semi-classical Hodge decomposition theorems for <inline-formula content-type="math/mathml"> ◻ s , k ( q ) \Box ^{(q)}_{s,k} </inline-formula> in some non-degenerate part of <inline-formula content-type="math/mathml"> Σ \Sigma </inline-formula> -- Szegö kernel asymptotics for lower energy forms -- Almost Kodaira embedding Theorems on CR manifolds -- Asymptotic expansion of the Szegö kernel -- Szegő kernel asymptotics and Kodairan embedding theorems on CR manifolds with transversal CR <inline-formula content-type="math/mathml"> S 1 S^1 </inline-formula> actions -- Szegő kernel asymptotics on some non-compact CR manifolds -- The proof of Theorem
- Cover -- Title page -- Chapter 1. Introduction and statement of the main results -- 1.1. Main results: Szegő kernel asymptotics for lower energy forms and almost Kodaira embedding Theorems on CR manifolds -- 1.2. Main results: Szegő kernel asymptotics -- 1.3. Main results: Szegő kernel asymptotics and Kodairan embedding theorems on CR manifolds with transversal CR ¹ actions -- Chapter 2. More properties of the phase ( , , ) -- Chapter 3. Preliminaries -- 3.1. Some standard notations -- 3.2. Set up and Terminology -- Chapter 4. Semi-classical \Box^{( )}_{ , } and the characteristic manifold for \Box^{( )}_{ , } -- Chapter 5. The heat equation for the local operatot \Box^{( )}_{ } -- 5.1. \Box^{( )}_{ } and the eikonal equation for \Box^{( )}_{ } -- 5.2. The transport equations for \Box^{( )}_{ } -- 5.3. Microlocal Hodge decomposition theorems for \Box^{( )}_{ } in -- 5.4. The tangential Hessian of ( , , ) -- Chapter 6. Semi-classical Hodge decomposition theorems for \Box^{( )}_{ , } in some non-degenerate part of Σ -- Chapter 7. Szegö kernel asymptotics for lower energy forms -- 7.1. Asymptotic upper bounds -- 7.2. Kernel of the spectral function -- 7.3. Szegö kernel asymptotics for lower energy forms -- Chapter 8. Almost Kodaira embedding Theorems on CR manifolds -- Chapter 9. Asymptotic expansion of the Szegö kernel -- Chapter 10. Szegő kernel asymptotics and Kodairan embedding theorems on CR manifolds with transversal CR ¹ actions -- 10.1. CR manifolds in projective spaces -- 10.2. Compact Heisenberg groups -- 10.3. Holomorphic line bundles over a complex torus -- Chapter 11. Szegő kernel asymptotics on some non-compact CR manifolds -- 11.1. The partial Fourier transform and the operator ^{( )}_{ , } -- 11.2. The small spectral gap property for \Box⁽⁰⁾_{ , } with respect to ⁽⁰⁾_{ , }
- 11.3. Szegő kernel asymptotics on Γ×\Real, where Γ=\Complexⁿ⁻¹ or Γ is a bounded strongly pseudoconvex domain in \Complexⁿ⁻¹ -- Chapter 12. The proof of Theorem 5.28 -- References -- Back Cover