Diameter bounds for convex surfaces with pinched mean curvature (Q1344926)

If the mean curvature \(H\) of a closed convex surface in \(\mathbb{R}^ 3\) is pinched by \({1\over 2} < c \leq H \leq 1\), then \(\text{diam}(K) < D(c)\). Here \(D(c)\) is a function expressed in terms of Delaunay surfaces which are used as comparison surfaces. For surfaces of revolution and \({1\over 2} \leq H \leq 1\) the author shows \(\text{diam}(K) < \pi + 2\) and conjectures that this is also true for surfaces not rotationally symmetric.