Perturbed, Genus One Scherk Surfaces and their limits

by Douglas, Casey, Ph.D., RICE UNIVERSITY, 2009, 118 pages; 3362149


The singly periodic, genus one helicoid is conjectured to be the limit of a one parameter family of doubly periodic minimal surfaces referred to as Perturbed Genus One Scherk Surfaces. Using elementary elliptic function theory, we show such surfaces exist, solving a two-dimensional period problem by perturbing a one-dimensional problem. Using flat structures associated to these minimal surfaces, we then verify the conjecture.

AdviserMichael Wolf
Source TypeDissertation
Publication Number3362149

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