Holomorphic Families of Strongly Pseudoconvex Domains in a Kähler Manifold

Choi, Young Sang; Yoo, Sungmin

doi:10.1007/s12220-020-00369-3

Cited by 2 publications

(2 citation statements)

References 13 publications

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“…Theorem 3.5 and Theorem 3.8 imply the following Corollary 3.9 (cf. Remark 3.4 in [12]). The fiberwise Kähler-Einstein metric ρ satisfies the equation…”

Section: Fiberwise Kähler-einstein Metricmentioning

confidence: 96%

Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains

Choi

Yoo

2022

Doc. Math.

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Let π : C n × C → C be the projection map onto the second factor and let D be a domain in C n+1 such that for y ∈ π(D), every fiber D y := D ∩ π −1 (y) is a smoothly bounded strongly pseudoconvex domain in C n and is diffeomorphic to each other. By Chau's theorem, the Kähler-Ricci flow has a long time solution ω y (t) on each fiber X y . This family of flows induces a smooth real (1,1)-form ω(t) on the total space D whose restriction to the fiber D y satisfies ω(t)| Dy = ω y (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 C n+1 .

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“…Theorem 3.5 and Theorem 3.8 imply the following Corollary 3.9 (cf. Remark 3.4 in [12]). The fiberwise Kähler-Einstein metric ρ satisfies the equation…”

Section: Fiberwise Kähler-einstein Metricmentioning

confidence: 96%

Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains

Choi

Yoo

2022

Doc. Math.

View full text Add to dashboard Cite

show abstract

“…Theorem 3.5 and Theorem 3.8 imply the following Corollary 3.9 (cf. Remark 3.4 in [13]). The fiberwise Kähler-Einstein metric ρ satisfies the equation…”

Section: 3mentioning

confidence: 96%

Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains

Choi¹,

Yoo²

2020

Preprint

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Let π : C n ×C → C be the projection map onto the second factor and let D be a domain in C n+1 such that for y ∈ π(D), every fiber D y := D ∩ π −1 (y) is a smoothly bounded strongly pseudoconvex domain in C n and is diffeomorphic to each other. By Chau's theorem, the Kähler-Ricci flow has a long time solution ω y (t) on each fiber X y . This family of flows induces a smooth real (1,1)-form ω(t) on the total space D whose restriction to the fiber D y satisfies ω(t)| Dy = ω y (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 C n+1 .

show abstract

Holomorphic Families of Strongly Pseudoconvex Domains in a Kähler Manifold

Cited by 2 publications

References 13 publications

Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains

Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains

Fiberwise Kähler-Ricci flows on families of bounded strongly pseudoconvex domains

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