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arXiv · 1710.09714

Prescribing sign-changing mean curvature candidates on the n+1-dimensional unit ball

Hong Zhang
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Abstract

This paper focuses on the problem of prescribing mean curvature on the unit ball. Assume that $f$, which is allowed to change sign, satisfies Morse index counting or certain kind of symmetry condition. By using a negative gradient flow method, we then prove that $f$ can be realized as the boundary mean curvature of some conformal metric.

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Hong Zhang. 2017-10-25. Prescribing sign-changing mean curvature candidates on the n+1-dimensional unit ball. https://arxiv.org/abs/1710.09714

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