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

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.

12 pages. Now published in Proc. Roy. Soc. Edinburgh Sect. A. Some typos are corrected

References in corpus (3)

• The Webster scalar curvature flow on CR sphere. Part I
• Prescribed scalar curvature plus mean curvature flows in compact manifolds with boundary of negative conformal invariant
• The Webster scalar curvature flow on CR sphere. Part II