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Proceedings of the American Mathematical Society Series B
Proceedings of the American Mathematical Society Series B
ISSN 2330-1511

 

Continuous leafwise harmonic functions on codimension one transversely isometric foliations


Author: Shigenori Matsumoto
Journal: Proc. Amer. Math. Soc. Ser. B 1 (2014), 53-61
MSC (2010): Primary 53C12; Secondary 37C85
Published electronically: April 29, 2014
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Abstract: Let $ \mathcal {F}$ be a codimension one foliation on a closed manifold $ M$ which admits a transverse dimension one Riemannian foliation. Then any continuous leafwise harmonic functions are shown to be constant on leaves.


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Additional Information

Shigenori Matsumoto
Affiliation: Department of Mathematics, College of Science and Technology, Nihon University, 1-8-14 Kanda, Surugadai, Chiyoda-ku, Tokyo, 101-8308 Japan
Email: matsumo@math.cst.nihon-u.ac.jp

DOI: http://dx.doi.org/10.1090/S2330-1511-2014-00008-0
PII: S 2330-1511(2014)00008-0
Keywords: Codimension one foliations, leafwise harmonic functions, stationary measures
Received by editor(s): June 4, 2013
Received by editor(s) in revised form: September 12, 2013
Published electronically: April 29, 2014
Additional Notes: The author was partially supported by Grant-in-Aid for Scientific Research (C) No. 25400096.
Communicated by: Yingfei Yi
Article copyright: © Copyright 2014 by the author under Creative Commons Attribution-Noncommercial 3.0 License (CC BY NC 3.0)