![Ilmanen’s “Planosphere” (~1994 & 2010). Complete, embedded of genus g. One non-compact end, asymptotic to a regular cone w/ 4g+g symmetries.
Ref.: [1] T. Ilmanen. Lectures on Mean Curvature Flow and Related Equations, Conference on Partial Differential Equations & Applications to Geometry, 1995, ICTP, Trieste. [2] N. Kapouleas, S. Kleene, N.M. Møller. Mean curvature self-shrinkers of high genus: Non-compact examples. [Rigorous proof of existence/construction via gluing. Link: arxiv:1106.5454]
Source: Embedded Mean Curvature Self-shrinkers in R^3, Niels Martin Møller, Department of Mathematics at MIT](http://www.tumblr.com/photo/1280/scienceisbeauty/13831876786/1/tumblr_lvsn02uAny1qaityk)
Ilmanen’s “Planosphere” (~1994 & 2010). Complete, embedded of genus g. One non-compact end, asymptotic to a regular cone w/ 4g+g symmetries.
Ref.: [1] T. Ilmanen. Lectures on Mean Curvature Flow and Related Equations, Conference on Partial Differential Equations & Applications to Geometry, 1995, ICTP, Trieste. [2] N. Kapouleas, S. Kleene, N.M. Møller. Mean curvature self-shrinkers of high genus: Non-compact examples. [Rigorous proof of existence/construction via gluing. Link: arxiv:1106.5454]
Source: Embedded Mean Curvature Self-shrinkers in R^3, Niels Martin Møller, Department of Mathematics at MIT