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Prescribed mean curvature equation on the unit ball in the presence of reflection or rotation symmetry

Published online by Cambridge University Press:  27 December 2018

Pak Tung Ho
Pak Tung Ho*
Affiliation:
Department of Mathematics, Sogang University, Seoul 121-742, Korea (paktungho@yahoo.com.hk; ptho@sogang.ac.kr)
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Abstract

Using the flow method, we prove some existence results for the problem of prescribing the mean curvature on the unit ball. More precisely, we prove that there exists a conformal metric on the unit ball such that its mean curvature is f, when f possesses certain reflection or rotation symmetry.

Keywords

mean curvatureunit ballNirenberg's problemPrimary 53C4453A30Secondary 35J9335B44
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 3 , June 2019 , pp. 781 - 794
Copyright
Copyright © Royal Society of Edinburgh 2018 

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Footnotes

Current address: Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton NJ 08544 USA Email address: ptho@princeton.edu

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