Universität zu Köln

Lu, Wen, Ma, Xiaonan and Marinescu, George ORCID: 0000-0001-6539-7860 (2020). Optimal convergence speed of Bergman metrics on symplectic manifolds. J. Symplectic Geom., 18 (4). S. 1091 - 1127. SOMERVILLE: INT PRESS BOSTON, INC. ISSN 1540-2347

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Abstract

It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high p-tensor powers of the prequantum line bundle. We show that the Fubini-Study forms induced by these embeddings converge at speed rate 1/p(2) to the symplectic form. This result implies the generalization to the almost-Kahler case of the lower bounds on the Calabi functional given by Donaldson for Kahler manifolds, as shown by Lejmi and Keller.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lu, Wen UNSPECIFIED UNSPECIFIED UNSPECIFIED Ma, Xiaonan UNSPECIFIED UNSPECIFIED UNSPECIFIED Marinescu, George UNSPECIFIED orcid.org/0000-0001-6539-7860 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-349773
Journal or Publication Title:	J. Symplectic Geom.
Volume:	18
Number:	4
Page Range:	S. 1091 - 1127
Date:	2020
Publisher:	INT PRESS BOSTON, INC
Place of Publication:	SOMERVILLE
ISSN:	1540-2347
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 LOWER BOUNDS; ASYMPTOTICS; POWERS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/34977