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 language | English |
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Journal | Complex Variables and Elliptic Equations |
Volume | 62 |
Issue number | 8 |
Pages (from-to) | 1037-1043 |
ISSN | 1747-6933 |
DOIs | |
Publication status | Published - 2017 |