Intrinsic derivative, curvature estimates and squeezing function

Zhang, Liyou

doi:10.1007/s11425-016-9043-8

Cited by 12 publications

(8 citation statements)

References 28 publications

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“…Fornaess and E. Wold constructed in [10] a bounded convex domain Ω, with C 2 boundary, which is not strongly pseudoconvex and whose squeezing function tends to one at the boundary. It follows from Theorem 1.1 in [37] and Theorem 4 in [18] that…”

Section: Introductionmentioning

confidence: 95%

The geometry of domains with negatively pinched Kähler metrics

Bracci¹,

Gaussier²,

Zimmer³

2018

Preprint

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We study how the existence of a negatively pinched Kähler metric on a domain in complex Euclidean space restricts the geometry of its boundary. In particular, we show that if a convex domain admits a complete Kähler metric, with pinched negative holomorphic bisectional curvature outside a compact set, then the boundary of the domain does not contain any complex subvariety of positive domain. Moreover, if the boundary of the domain is smooth, then it is of finite type in the sense of D'Angelo. We also use curvature to provide a characterization of strong pseudoconvexity amongst convex domains. In particular, we show that a convex domain with C 2,α boundary is strongly pseudoconvex if and only if it admits a complete Kähler metric with sufficiently tight pinched negative holomorphic sectional curvature outside a compact set. B(g)(X, Yand the holomorphic sectional curvature of a non-zero X ∈ T p M is given byWe say that (M, g) has pinched negative holomorphic bisectional curvature if there exists a, b > 0 such that −a ≤ B(g)(X, Y ) ≤ −b for all p ∈ M and non-zero vectors X, Y ∈ T p M . Likewise, we say that (M, g) has pinched negative holomorphic sectional curvature if there exists a, b > 0 such that −a ≤ H(g)(X) ≤ −b

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Section: Introductionmentioning

confidence: 95%

The geometry of domains with negatively pinched Kähler metrics

Bracci¹,

Gaussier²,

Zimmer³

2018

Preprint

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“…[6,10,18,20]). For more details on various recent results, we refer the readers to the survey papers [7,25].…”

Section: Introductionmentioning

confidence: 99%

On the generalized squeezing functions and Fridman invariants of special domains

Rong¹,

Yang²

2021

Preprint

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“…It is clear from the definitions that both Fridman invariants and generalized squeezing functions are invariant under biholomorphisms, and both take value in (0, 1]. There have been much study on the Fridman invariant and the squeezing function in recent years, and we refer the readers to two recent survey articles [13,3] and the references therein for various aspects of the current research on this subject.…”

Section: Introductionmentioning

confidence: 99%