Note on Brendle-Eichmair's paper "Isoperimetric and Weingarten surfaces   in the Schwarchild manifold"
  In this short note, we show that the assumption "convex" in Theorem 7 of Brendle-Eichmair's paper \cite{BE} is unnecessary. 
Haizhong Li, Yong Wei, Changwei Xiong
math.DG