Functions holomorphic along holomorphic vector fields

Kang Tae Kim, Evgeny Poletsky, Gerd Schmalz

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

The main result of the paper is the following generalization of Forelli's theorem (Math. Scand. 41:358-364, 1977): Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with eigenvalues whose ratios are positive reals. Then any function θ that has an asymptotic Taylor expansion at p and is holomorphic along the complex integral curves of F is holomorphic in a neighborhood of p. We also present an example to show that the requirement for ratios of the eigenvalues to be positive reals is necessary.

Original languageEnglish (US)
Pages (from-to)655-666
Number of pages12
JournalJournal of Geometric Analysis
Volume19
Issue number3
DOIs
StatePublished - Jul 2009

Keywords

  • Holomorphic functions
  • Holomorphic vector fields

ASJC Scopus subject areas

  • Geometry and Topology

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