Minimal Surface Linear Combinatoin Theorem
Dorff, Michael · Taylor, Stephen
Original · EN
Given two univalent harmonic mappings f₁ and f₂ on D, which lift to minimal surfaces via the Weierstrass-Enneper representation theorem, we give necessary and sufficient conditions for f₃=(1-s)f₁+sf₂ to lift to a minimal surface for s∈[0,1]. We then construct such mappings from Enneper's surface to Scherk's singularly periodic surface, Sckerk's doubly periodic surface to the catenoid, and the 4-Enneper surface to the 4-noid.
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