Kakutani's theorem for real-valued maps on a compact surface

Authors:
E. H. Kronheimer and P. B. Kronheimer

Journal:
Proc. Amer. Math. Soc. **85** (1982), 256-260

MSC:
Primary 53A05

MathSciNet review:
652453

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Abstract: Let be a compact -manifold (without boundary) -embedded in . Then there exists positive such that, given any positive and any continuous map , there exist points ,,, satisfying in the euclidean norm, for which .

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DOI:
https://doi.org/10.1090/S0002-9939-1982-0652453-0

Article copyright:
© Copyright 1982
American Mathematical Society