In this talk I will present recent joint work with Bourni and Langford. We prove that for any \( 0< A<\pi /2\) there exists a strictly convex translating solution of mean curvature flow in \(\mathbb{R}^n\) contained in a slab of width \(\pi/cosA\) and in no smaller slab.

In this talk I will discuss the significance of curvature estimates for constant mean curvature surfaces, present some classical ones and their applications.

In this talk I will discuss recent results on the geometry of constant mean curvature ($H\neq 0$) surfaces embedded in $\mathbb{R}^3$. Among other things I will prove a radius and curvature estimates for constant mean curvature disks embedded in $\mathbb{R}^3$. It follows from the radius estimate that the only complete constant mean curvature disk embedded in $\mathbb{R}^3$ is the round sphere.
This is joint work with Bill Meeks.