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arXiv · 1812.00806

Checking real analyticity on surfaces

Jacek Bochnak·János Kollár·Wojciech Kucharz
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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 the 2-sphere 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.

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BibTeXRIS

Jacek Bochnak, János Kollár, Wojciech Kucharz. 2018-12-03. Checking real analyticity on surfaces. https://arxiv.org/abs/1812.00806

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