A necessary condition for prescribing mean curvature equations in 𝔹ⁿ

Liu, Chenkai; Wang, Shaodong

doi:10.1090/proc/16023

A necessary condition for prescribing mean curvature equations in $\mathbb {B}^n$
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by Chenkai Liu and Shaodong Wang

Proc. Amer. Math. Soc. 150 (2022), 4831-4839

DOI: https://doi.org/10.1090/proc/16023

Published electronically: May 6, 2022

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Abstract:

Let $(\mathbb {B}^n,g_0)$ be the $n$-dimensional Euclidean unit ball with $n\geqslant 3$. We obtain a necessary condition on the existence of conformal metric in $\mathbb {B}^n$ with zero scalar curvature and prescribed mean curvature function on the boundary.

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