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On univalent harmonic
mappings and minimal surfaces
Allen Weitsman |
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Vol. 192 (2000), No. 1, 191–200
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Abstract |
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If S is the graph of a minimal surface, then when given parametrically by the Weierstrass representation, the first two coordinate functions give a univalent harmonic mapping. In this paper, the starting point is a univalent harmonic mapping f of the unit disk U. A height function is defined on an appropriate Riemann surface over the range of f which satisfies the minimal surface equation away from the branch points. This height function is then used to obtain function theoretic information about f. |
Milestones
Received: 9 March 1998
Published: 1 January 2000
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Authors |
| Allen Weitsman | |
| Purdue University West Lafayette, IN 47907-1395 |
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