A general Schwarz lemma for almost-Hermitian manifolds

Valentino Tosatti

Research output: Contribution to journalArticlepeer-review


We prove a version of Yau's Schwarz lemma for general almost-complex manifolds equipped with almost-Hermitian metrics. This requires an extension to this setting of the Laplacian comparison theorem. As an application, we show that the product of two almost-complex manifolds does not admit any complete almost-Hermitian metric with bisectional curvature bounded between two negative constants that satisfies some additional assumptions.

Original languageEnglish (US)
Pages (from-to)1063-1086
Number of pages24
JournalCommunications in Analysis and Geometry
Issue number5
StatePublished - Dec 2007

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Geometry and Topology
  • Statistics, Probability and Uncertainty


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