Hong, Jiaxing On interior estimates for mean curvature of convex surfaces in \(\mathbb R^3\) and its applications. (English) Zbl 1303.53015 Ge, Molin (ed.) et al., Frontiers in differential geometry, partial differential equations and mathematical physics. In memory of Gu Chaohao. Hackensack, NJ: World Scientific (ISBN 978-981-4578-07-3/hbk; 978-981-4578-08-0/pbk). 105-124 (2014). Summary: In the present paper a direct proof for the interior estimates for mean curvature of convex surfaces in \(\mathbb R^3\) is given. Meanwhile, when the Gaussian curvature of such a \(C^2\)-convex surface is degenerate on the boundary at degree \(m\) where \(m\) is some integer, a global lower bound away from zero for mean curvature is also obtained. Therefore, global smooth isometric embedding for smooth positive disks in \(\mathbb R^3\) can be constructed by means of the techniques in [J. Hong et al., Commun. Partial Differ. Equations 36, No. 4–6, 635–656 (2011; Zbl 1232.35076)].For the entire collection see [Zbl 1291.00056]. MSC: 53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature Keywords:convex surfaces; bound away from zero; mean curvature Citations:Zbl 1232.35076 PDFBibTeX XMLCite \textit{J. Hong}, in: Frontiers in differential geometry, partial differential equations and mathematical physics. In memory of Gu Chaohao. Hackensack, NJ: World Scientific. 105--124 (2014; Zbl 1303.53015) Full Text: DOI