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arXiv · 1311.5004

Constructions of minimal periodic surfaces and minimal annuli in Sol3

Christophe Desmonts
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Abstract

We construct two one-parameter families of minimal properly embedded surfaces in the Lie group Sol3 using a Weierstrass-type representation. These surfaces are not invariant by a one-parameter group of ambient isometries. The first one can be viewed as a family of helicoids, and the second one is a family of minimal annuli called catenoids. Finally we study limits of these catenoids, and in particular we show that one of these limits is a new minimal entire graph.

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Christophe Desmonts. 2013-11-20. Constructions of minimal periodic surfaces and minimal annuli in Sol3. https://doi.org/10.2140/pjm.2015.276.143

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