Constant mean curvature surfaces with $D_4$-singularities

Ogata, Yuta; Teramoto, Keisuke

doi:10.2969/aspm/07810345

VOL. 78 | 2018 Constant mean curvature surfaces with $D_4$-singularities

Yuta Ogata, Keisuke Teramoto

Editor(s) Shyuichi Izumiya, Goo Ishikawa, Minoru Yamamoto, Kentaro Saji, Takahiro Yamamoto, Masatomo Takahashi

Adv. Stud. Pure Math., 2018: 345-363 (2018) DOI: 10.2969/aspm/07810345

Abstract

We study $D_4$-singularities of constant mean curvature (CMC) surfaces in Riemannian and semi-Riemannian spaceforms. We will give criteria for $D_4^{-}$-singularities, which are related to the Hopf differential. We also show the non-existence of (spacelike) CMC surfaces with $D_4^+$-singularities.