Checking real analyticity on surfaces
Classical Analysis and ODEs
2018-12-04 v1 Algebraic Geometry
Differential Geometry
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.
Cite
@article{arxiv.1812.00806,
title = {Checking real analyticity on surfaces},
author = {Jacek Bochnak and János Kollár and Wojciech Kucharz},
journal= {arXiv preprint arXiv:1812.00806},
year = {2018}
}