Let $\Sigma$ be a closed and embedded surface of $\mathbb{R}^3$. Since it must be orientable, let $N$ be a unit normal for $\Sigma$ pointing towards the bounded component of $\mathbb{R}^3 \setminus \Sigma$. Is it possible that $\Sigma$ has negative total mean curvature, that is,
$$\int_\Sigma H \, \mathrm{d}A < 0?$$
I adopt the convention that the unit sphere $\mathbb{S}^2 \subset \mathbb{R}^3$ has mean curvature equal to $1$ when such a choice of normal has been made.