Vol. 101, No. 2, 1982

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A note on the Gauss curvature of harmonic and minimal surfaces

Giorgio Talenti

Vol. 101 (1982), No. 2, 477–492

We present some inequalities for the Gauss curvature of embedded surfaces in euclidean 3-space, which are either graphs of harmonic functions or minimal. The proofs exploit the following facts: (i) a partial differential equation constrains the curvature of the surfaces in question; (ii) the differential equation constrains in a significant way, via an isoperimetric inequality, the level lines of the curvature.

Mathematical Subject Classification 2000
Primary: 53A10
Secondary: 53C42
Received: 2 February 1981
Published: 1 August 1982
Giorgio Talenti