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.