Scalar curvature and convexity

Question

Let $D \subset \mathbb{R}^d$ be a $C^2$ bounded domain and $n(x)$ the outer unit normal field. The scalar (mean) curvature is defined sometimes as $$H(x)=\mathrm{div}\, n(x), \quad x\in \partial D$$ and sometimes as $$H'(x)=\mathrm{div}_{\partial D}\, n(x) \quad x\in \partial D.$$ I have two questions:

1. Are the above definitions the same?

2. When $D$ is convex, is it true that $H(x)\ge 0$ at $\partial D$?

I'm looking for the proof or a reference where I can find such results.