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Seminários do IMPA

Geometria Diferencial

Construction of genus one helicoids in $\mathbb{H}^2 \times \mathbb{R}$
Ivan Passoni

Terça-feira, 22 de janeiro de 2019, 15:30
Sala 236.

In 2004, Weber, Hoffman and Wolf constructed a complete, properly embebbed minimal surface of genus one in $\mathbb{R}^3$ with one end that is asymptotic to the end of a Helicoid. In 2013, Hoffman, Traizet and White extended this result for $\mathbb{S}^2 \times \mathbb{R}$, that is, they showed that for every genus $g$, there is a complete properly embedded genus $g$ minimal surface in $\mathbb{S}^2 \times \mathbb{R}$ with two ends, these ends asymptotic to helicoids of any prescribed pitch. In this seminar we present the similar result in $\mathbb{H}^2 \times \mathbb{R}$ for the genus one case. That is, we construct a properly embedded minimal surfaces in $\mathbb{H}^2 \times \mathbb{R}$ of genus one with one end, this end asymptotic to the end of a helicoid of prescribed pitch. We also construct screw-motion invariant minimal surfaces asymptotic to the helicoid that have genus one in the quotient.