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A curvature formula associated to a family of pseudoconvex domains

Xu Wang (Institutionen för matematiska vetenskaper, Algebra och geometri)
Annales de l'Institut Fourier (0373-0956). Vol. 67 (2017), 1, p. 269-313.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Brunn-Minkowski theory, Prekopa theorem, partial derivative-equation, Hormander theory, direct image bundles, bergman-kernel, holomorphic motions, complex, structures, vector-bundles, positivity, equation, metrics, theorem, deformations, Mathematics, mailly jp, 1982, annales scientifiques de l ecole normale superieure, v15, p457, MAILLY J.-P., Complex analytic and differential geometry, LLAND G. B., 1972, The Neumann problem for the Cauchy-Riemann complex, V75, ekopa a, 1973, acta scientiarum mathematicarum, v34, p334, IGER T., 2015, Curvature of higher direct image sheaves



Denna post skapades 2017-04-03.
CPL Pubid: 248777

 

Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, Algebra och geometriInstitutionen för matematiska vetenskaper, Algebra och geometri (GU)

Ämnesområden

Matematik

Chalmers infrastruktur