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A note on the Gauss
curvature of harmonic and minimal surfaces
Giorgio Talenti |
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Vol. 101 (1982), No. 2, 477–492
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Abstract |
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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
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Milestones
Received: 2 February 1981
Published: 1 August 1982
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Authors |
| Giorgio Talenti | |
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