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nirenberg's problem

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Prescribed mean curvature equation on the unit ball in the presence of reflection or rotation symmetry
Pak Tung Ho
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 3 / June 2019

Published online by Cambridge University Press:

27 December 2018, pp. 781-794

Print publication:

June 2019
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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.