A necessary condition for prescribing mean curvature equations in 𝔹ⁿ

Abstract

Let ( B n , g 0 ) (\mathbb {B}^n,g_0) be the n n -dimensional Euclidean unit ball with n ⩾ 3 n\geqslant 3 . We obtain a necessary condition on the existence of conformal metric in B n \mathbb {B}^n with zero scalar curvature and prescribed mean curvature function on the boundary.