Remarks on the boundary curve of a constant mean curvature topological disc. Issue 8 (3rd August 2017)

• Record Type: Journal Article
• Authors: Brander, David; Lopéz, Rafael
• Is Part Of: Complex variables and elliptic equations. Volume 62:Issue 8(2017)
• Page Start: 1037
• Page End: 1043
• Publication Date: 2017-08-03
• Subjects: Constant mean curvature -- holomorphic quadratic differentials -- capillary surface; Primary: 53A10 -- 49Q10 -- Secondary: 35J60 -- 76D45; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2016.1260558
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : We discuss some consequences of the existence of the holomorphic quadratic Hopf differential on a conformally immersed constant mean curvature topological disc with analytic boundary. In particular, we derive a formula for the mean curvature as a weighted average of the normal curvature of the boundary curve, and a condition for the surface to be totally umbilic in terms of the normal curvature.