A curvature formula associated to a family of pseudoconvex domains
Artikel i vetenskaplig tidskrift, 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.

1973

metrics

deformations

The Neumann problem for the Cauchy-Riemann complex

Complex analytic and differential geometry

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1972

direct image bundles

annales scientifiques de l ecole normale superieure

Curvature of higher direct image sheaves

equation

vector-bundles

LLAND G. B.

positivity

Brunn-Minkowski theory

Prekopa theorem

p334

IGER T.

theorem

bergman-kernel

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Hormander theory

structures

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complex

MAILLY J.-P.

holomorphic motions

acta scientiarum mathematicarum

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v34

1982

partial derivative-equation

2015

mailly jp

v15

Författare

Xu Wang

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Algebra och geometri

Annales de lInstitut Fourier

0373-0956 (ISSN)

Vol. 67 1 269-313

Ämneskategorier

Matematik

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2017-10-07