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Article overview
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A curvature formula associated to a family of pseudoconvex domains | Xu Wang
; | Date: |
2 Aug 2015 | Abstract: | Inspired by Berndtsson’s results cite{Bern06} and cite{Bern09}, we shall
define the curvature operator $Theta_{jar k}$ for a family of weighted
Bergman spaces associated to a family of smoothly bounded strongly pseudoconvex
domains ${D_t}$. What’s more, we shall introduce the notion of geodesic
curvature, say $ heta_{jar k}(
ho)$, for ${D_t}$ and use it to decode the
boundary term of the curvature formula. In particular, we get the
$partialdbar$-Bochner type variation formula for the Bergman projection. A
flatness criterion for $Theta_{jar k}$ and its applications are also given
in this paper. | Source: | arXiv, 1508.0242 | Services: | Forum | Review | PDF | Favorites |
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