Convexity on complex hyperbolic space

Judit Abardia, Eduardo Gallego

Research output: Contribution to journalArticleResearchpeer-review

Abstract

In a Riemannian manifold a regular convex domain is said to be λ-convex if its normal curvature at each point is greater than or equal to λ < 0. In a Hadamard manifold, the asymptotic behaviour of the quotient vol(Ωt)/vol(∂Ωt)for a family of λ-convex domains Ωt expanding over the whole space has been studied and general bounds for this quotient are known. In this paper we improve this general result in the complex hyperbolic space ℂH n(-4k2), a Hadamard manifold with constant holomorphic curvature equal to - 42. Furthermore, we give some specific properties of convex domains in ℂHn(-4k2)and we prove that λ-convex domains of arbitrary diameter exists if λ ≤ k. © Heldermann Verlag.
Original languageEnglish
Pages (from-to)329-338
JournalJournal of Convex Analysis
Volume20
Issue number2
Publication statusPublished - 14 Aug 2013

Keywords

  • Area
  • Complex hyperbolic space
  • Convex domain
  • Volume

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