Weierstrass type representations

Mason Pember (Politecnico di Torino, Italy)

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Jan 28, 2020
from 02:00 PM to 03:00 PM



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Abstract: In the 19th century, Weierstrass and Enneper developed a representation formula for minimal surfaces in Euclidean 3-space. This formula has been fundamental in the creation of many interesting examples of minimal surfaces. Since then several similar representations have been developed for other classes of surfaces in 3 dimensional space forms such as constant mean curvature 1 surfaces in hyperbolic 3-space. All of these representations have the same basic ingredients: a meromorphic function and a holomorphic 1-form. It is therefore natural to ask if these representations can be unified in some way. In this talk we will outline a unified geometric way of viewing these representations via the transformation theory of Omega surfaces.

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