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arXiv · 1910.05809

Convexity of constant mean curvature graphs in $\mathbb{R}^{n+1}$ with planar boundary

Joel Spruck·Liming Sun
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Abstract

We study the Dirichlet problem for a graph $Σ$ in $\mathbb{R}^{n+1}$ with normalized constant mean curvature $H>0$ and planar boundary $Γ=\partial Ω$. Our main result is that the optimal solvability condition, namely that the normalized mean curvature $h$ of $Γ$ satisfies $h\geq H$, also suffices when $Ω$ is strictly convex, to prove the strict convexity of $Σ$.

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Joel Spruck, Liming Sun. 2020-04-19. Convexity of constant mean curvature graphs in $\mathbb{R}^{n+1}$ with planar boundary. https://arxiv.org/abs/1910.05809

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