A curvature formula associated to a family of pseudoconvex domains
Journal article, 2017
We shall give a definition of the curvature operator for a family of weighted Bergman spaces {H-t} associated to a smooth family of smoothly bounded strongly pseudoconvex domains {D-t}. In order to study the "boundary term" in the curvature operator, we shall introduce the notion of geodesic curvature for the associated family of boundaries {delta D-t} As an application, we get a variation formula for the norms of Bergman projections of currents with compact support. A flatness criterion for {H(t)1 and its applications to triviality of fibrations are also given in this paper.
partial derivative-equation
structures
MAILLY J.-P.
theorem
ekopa a
direct image bundles
metrics
Mathematics
Prekopa theorem
1982
Hormander theory
complex
positivity
vector-bundles
IGER T.
v15
bergman-kernel
annales scientifiques de l ecole normale superieure
mailly jp
p457
p334
holomorphic motions
deformations
V75
equation
Curvature of higher direct image sheaves
1972
v34
Brunn-Minkowski theory
acta scientiarum mathematicarum
Complex analytic and differential geometry
2015
LLAND G. B.
1973
The Neumann problem for the Cauchy-Riemann complex
Author
Xu Wang
University of Gothenburg
Chalmers, Mathematical Sciences, Algebra and geometry
Annales de lInstitut Fourier
0373-0956 (ISSN)
Vol. 67 1 269-313Subject Categories (SSIF 2011)
Mathematics
DOI
10.5802/aif.3082