Checking real analyticity on surfaces

Jacek Bochnak, János Kollár, Wojciech Kucharz

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

We prove that a real-valued function (that is not assumed to be continuous) on a real analytic manifold is analytic whenever all its restrictions to analytic submanifolds homeomorphic to S2 are analytic. This is a real analog for the classical theorem of Hartogs that a function on a complex manifold is complex analytic iff it is complex analytic when restricted to any complex curve.

Original languageEnglish (US)
Pages (from-to)167-171
Number of pages5
JournalJournal des Mathematiques Pures et Appliquees
Volume133
DOIs
StatePublished - Jan 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Keywords

  • Homogeneous polynomial
  • Real analytic function
  • Real analytic manifold

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