Remarks on the boundary curve of a constant mean curvature topological disc

David Brander, Rafael Lopéz

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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.
Original languageEnglish
JournalComplex Variables and Elliptic Equations
Volume62
Issue number8
Pages (from-to)1037-1043
ISSN1747-6933
DOIs
Publication statusPublished - 2017

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