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arXiv · 2105.06774

Discrete Weierstrass-type representations

Mason Pember·Denis Polly·Masashi Yasumoto
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Abstract

Discrete Weierstrass-type representations yield a construction method in discrete differential geometry for certain classes of discrete surfaces. We show that the known discrete Weierstrass-type representations of certain surface classes can be viewed as applications of the $\Omega$-dual transform to lightlike Gauss maps in Laguerre geometry. From this construction, further Weierstrass-type representations arise. As an application of the techniques we develop, we show that all discrete linear Weingarten surfaces of Bryant or Bianchi type locally arise via Weierstrass-type representations from discrete holomorhpic maps.

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Mason Pember, Denis Polly, Masashi Yasumoto. 2021-05-14. Discrete Weierstrass-type representations. https://doi.org/10.1007/s00454-022-00439-z

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