Suppose is a translator in direction. Denote and is the second fundamental form of . Then it is well known that

Choose a local orthonormal frame such that , and in the neighborhood of some point . We want to change (1) to some expression on or . To do that, we need to apply both sides of (1) to , getting

where we have used . Similarly

Now let us calculate the Laplacian of second fundamental form

Then

Combining all the above estimates to (1), we get

where we write . Using this equation and the other one on , one can derive that if is mean convex then it is actually convex.