Curvature estimates in dimensions 2 and 3 for the level sets of -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

Published electronically:
April 25, 2012

MathSciNet review:
2922603

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Abstract | References | Similar Articles | Additional Information

Abstract: Sharp curvature estimates are given for the level sets of a class of -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