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Yoo, Sungmin
복소기하학 연구단
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FIBERWISE KÄHLER-RICCI FLOWS ON FAMILIES OF BOUNDED STRONGLY PSEUDOCONVEX DOMAINS

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Title
FIBERWISE KÄHLER-RICCI FLOWS ON FAMILIES OF BOUNDED STRONGLY PSEUDOCONVEX DOMAINS
Author(s)
Choi, Young-Jun; Sungmin Yoo
Publication Date
2022-01
Journal
Documenta Mathematica, v.27, pp.847 - 868
Publisher
Deutsche Mathematiker Vereinigung
Abstract
© 2022Let π: Cn × C → C be the projection map onto the second factor and let D be a domain in Cn+1 such that for y ∈ π(D), every fiber Dy: = D ∩ π−1(y) is a smoothly bounded strongly pseudoconvex domain in Cn and is diffeomorphic to each other. By Chau’s theorem, the Kähler-Ricci flow has a long time solution ωy(t) on each fiber Xy. This family of flows induces a smooth real (1,1)-form ω(t) on the total space D whose restriction to the fiber Dy satisfies ω(t)|Dy = ωy(t). In this paper, we prove that ω(t) is positive for all t > 0 in D if ω(0) is positive. As a corollary, we also prove that the fiberwise Kähler-Einstein metric is positive semi-definite on D if D is pseudoconvex in Cn+1.
URI
https://pr.ibs.re.kr/handle/8788114/12211
DOI
10.25537/dm.2022v27.847-868
ISSN
1431-0635
Appears in Collections:
Center for Complex Geometry (복소기하학 연구단) > 1. Journal Papers (저널논문)
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