Generalized Henneberg stable minimal surfaces

Seminario de Geometría

Speaker: David Moya

Abstract: In this talk we generalized the classical Henneberg minimal surface by giving an infinite family of complete, finitely branched, non-orientable, stable minimal surfaces in $\mathbb{R}^3$. These surfaces can be grouped into subfamilies depending on a positive integer $m$, which essentially measures the number of branch points. We describe the isometry group of the most symmetric example $H_m$. The surfaces $H_m$ can also be seeing either as the unique solution to a Björling problem for an hypocycloid of $m+1$ cups if $m$ is even or as the conjugate minimal surface to the unique solution to a Björling problem for an hypocycloid of $2m+2$ cups if $m$ is odd.