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Curvature estimates in dimensions 2 and 3 for the level sets of $ p$-harmonic functions in convex rings


Authors: Jürgen Jost, Xi-Nan Ma and Qianzhong Ou
Journal: Trans. Amer. Math. Soc. 364 (2012), 4605-4627
MSC (2010): Primary 35J05
DOI: https://doi.org/10.1090/S0002-9947-2012-05436-5
Published electronically: April 25, 2012
MathSciNet review: 2922603
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Abstract: Sharp curvature estimates are given for the level sets of a class of $ p$-harmonic functions in two and three dimensional convex rings.


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Additional Information

Jürgen Jost
Affiliation: Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, D-04103 Leipzig, Germany
Email: jjost@mis.mpg.de

Xi-Nan Ma
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, 230026, Anhui Province, People’s Republic of China
Email: xinan@ustc.edu.cn

Qianzhong Ou
Affiliation: Department of Mathematics, Hezhou University, Hezhou, 542800, Guangxi Province, People’s Republic of China
Email: ouqzh@163.com

DOI: https://doi.org/10.1090/S0002-9947-2012-05436-5
Keywords: Curvature estimates, level sets, harmonic function.
Received by editor(s): January 12, 2009
Received by editor(s) in revised form: July 20, 2010
Published electronically: April 25, 2012
Additional Notes: The research of the second author was supported by NSFC No.10671186 and “BaiRen Program in Chinese Academy of Sciences”.
The research of the third author was supported by Guangxi Natural Science Foundation 2010GXNSFA013123
Article copyright: © Copyright 2012 American Mathematical Society