Checking real analyticity on surfaces

Jacek Bochnak, János Kollár, Wojciech Kucharz

Research output: Contribution to journalArticle

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

Fingerprint

Analyticity
Curve Complex
Complex Manifolds
Homeomorphic
Submanifolds
Restriction
Analogue
Theorem

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • Mathematics(all)

Keywords

  • Homogeneous polynomial
  • Real analytic function
  • Real analytic manifold

Cite this

Bochnak, Jacek ; Kollár, János ; Kucharz, Wojciech. / Checking real analyticity on surfaces. In: Journal des Mathematiques Pures et Appliquees. 2020 ; Vol. 133. pp. 167-171.
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Checking real analyticity on surfaces. / Bochnak, Jacek; Kollár, János; Kucharz, Wojciech.

In: Journal des Mathematiques Pures et Appliquees, Vol. 133, 01.2020, p. 167-171.

Research output: Contribution to journalArticle

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