Universität zu Köln

Hsiao, Chin-Yu and Marinescu, George ORCID: 0000-0001-6539-7860 (2017). ON THE SINGULARITIES OF THE SZEGO PROJECTIONS ON LOWER ENERGY FORMS. J. Differ. Geom., 107 (1). S. 83 - 156. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1945-743X

Full text not available from this repository.

Abstract

Let X be an abstract not necessarily compact orientable CR manifold of dimension 2n - 1, n >= 2. Let rectangle((q))(b) be the Gaffney extension of Kohn Laplacian on (0, q)-forms. We show that the spectral function of rectangle((q))(b) admits a full asymptotic expansion on the non-degenerate part of the Levi form. As a corollary, we deduce that if X is compact and the Levi form is non-degenerate of constant signature on X, then the spectrum of rectangle((q))(b) in ]0, infinity[ consists of point eigenvalues of finite multiplicity. Moreover, we show that a certain microlocal conjugation of the associated Szego kernel admits an asymptotic expansion under a local closed range condition. As applications, we establish the Szego kernel asymptotic expansions on some weakly pseudoconvex CR manifolds and on CR manifolds with transversal CR S-1 actions. By using these asymptotics, we establish some local embedding theorems on CR manifolds and we give an analytic proof of a theorem of Lempert asserting that a compact strictly pseudoconvex CR manifold of dimension three with a transversal CR S-1 action can be CR embedded into C-N, for some N is an element of N.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Hsiao, Chin-Yu UNSPECIFIED UNSPECIFIED UNSPECIFIED Marinescu, George UNSPECIFIED orcid.org/0000-0001-6539-7860 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-219775
Journal or Publication Title:	J. Differ. Geom.
Volume:	107
Number:	1
Page Range:	S. 83 - 156
Date:	2017
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1945-743X
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PSEUDOCONVEX CR MANIFOLDS; BERGMAN-KERNEL; LINE BUNDLES; SYMPLECTIC-MANIFOLDS; TOEPLITZ-OPERATORS; DOMAINS; QUANTIZATION; ASYMPTOTICS; BOUNDARIES; EXISTENCE Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21977