A gap theorem for the complex geometry of convex domains

DOI10.1090/tran/7284zbMath1405.32053arXiv1609.07050OpenAlexW2963163520MaRDI QIDQ4580365

Andrew M. Zimmer

Publication date: 15 August 2018

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.07050

zbMATH Keywords

holomorphic sectional curvatureBergman metricsqueezing functionstrongly pseudoconvex domains

Mathematics Subject Classification ID

Invariant metrics and pseudodistances in several complex variables (32F45) Kähler manifolds (32Q15) Rigidity results (53C24) Strongly pseudoconvex domains (32T15)

Related Items (18)

Subelliptic estimates from Gromov hyperbolicity ⋮ On the generalized squeezing functions and Fridman invariants of special domains ⋮ Squeezing function corresponding to polydisk ⋮ On the squeezing function for finitely connected planar domains ⋮ Boundary behavior of the Carathéodory and Kobayashi-Eisenman volume elements ⋮ On boundary points at which the squeezing function tends to one ⋮ A comparison of two biholomorphic invariants ⋮ Holomorphic invariants of bounded domains ⋮ On the squeezing function and Fridman invariants ⋮ A non-strictly pseudoconvex domain for which the squeezing function tends to 1 towards the boundary ⋮ The squeezing function on doubly-connected domains via the Loewner differential equation ⋮ Some properties of \(h\)-extendible domains in \(\mathbb{C}^{n + 1} \) ⋮ Fridman function, injectivity radius function, and squeezing function ⋮ Characterizing strong pseudoconvexity, obstructions to biholomorphisms, and Lyapunov exponents ⋮ Fridman's invariant, squeezing functions, and exhausting domains ⋮ The automorphism group and limit set of a bounded domain II: the convex case ⋮ On some properties of the squeezing function corresponding to polydisk ⋮ Boundary behavior of the squeezing functions of ℂ-convex domains and plane domains

Cites Work

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• Gromov hyperbolicity and the Kobayashi metric on convex domains of finite type
• Some properties of squeezing functions on bounded domains
• Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type
• Geometry of domains with the uniform squeezing property
• Characterization of convex domains with noncompact automorphism group
• Canonical metrics on the moduli space of Riemann surfaces. I
• Properties of squeezing functions and global transformations of bounded domains
• Convex Domains and Kobayashi Hyperbolicity
• Constant Holomorphic Curvature
• On the Structure of a Certain Class of Kaehler Varieties

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