# King's College London

## One-sided curvature estimates for \$H\$-disks.

Research output: Contribution to journalArticle

William H. Meeks III, Giuseppe Tinaglia

Original language English 479-503 Cambridge Journal of Mathematics 8 https://doi.org/10.4310/CJM.2020.v8.n3.a2 12 Jun 2020 2 Oct 2020

## Abstract

In this paper we prove a one-sided curvature estimate for disks embedded in R3 with constant mean curvature. An important feature of this estimate is its independence on the value of the constant mean curvature. For clarity of exposition, we will call an oriented surface Σ immersed in R 3 an H-surface if it is embedded, connected and it has non-negative constant mean curvature H. We will call an H-surface an H-disk if the H-surface is homeomorphic to a closed unit disk in the Euclidean plane. We remark that this definition of H-surface differs from the one given in [? ], where we restricted to the case where H > 0. In this paper B(R) denotes the open ball in R3 centered at the origin ~0 of radius R, B(R) denotes its closure and for a point p on a surface Σ in R3, |AΣ|(p) denotes the norm of the second fundamental form of Σ at p.

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