On curvature estimates for constant mean curvature surfaces

Abstract

We derive extrinsic curvature estimates for compact disks embedded in R 3 with nonzero constant mean curvature.Mathematics Subject Classification: Primary 53A10, Secondary 49Q05, 53C42

The geometry of constant mean curvature surfaces in $\mathbb{R}^3$

“…We wish to emphasize to the reader that the curvature estimates for embedded constant mean curvature disks given in Theorem 1.3 depend only on the lower positive bound H for their mean curvature. Previous important examples of curvature estimates for constant mean curvature surfaces, assuming certain geometric conditions, can be found in the literature; see for instance [3,4,6,10,11,35,36,37,38,40,41].…”

Curvature estimates for constant mean curvature surfaces

“…We wish to emphasize to the reader that the curvature estimates for embedded constant mean curvature disks given in Theorem 1.1 depend only on the lower positive bound H for their mean curvature. Previous important examples of curvature estimates for constant mean curvature surfaces, assuming certain geometric conditions, can be found in the literature; see for instance [2,3,4,9,10,27,28,29,30,34,35].…”