DPW Potentials for Compact Symmetric CMC Surfaces in ${\mathbb{S}}^3$

Abstract

Inspired by the work of Heller [12], we show that there exists a DPW potential for the Lawson surface ${\xi }_{k-1,l-1}$ from which it is possible to reconstruct the minimal immersion $f:{\xi }_{k-1,l-1}\to {\mathbb{S}}^3$ via the DPW method. Moreover, we extend the result to surfaces immersed in the 3-sphere with constant mean curvature which satisfy a certain symmetric condition.

20 pages, to appear in Journal of Geometry and Physics

References in corpus (2)

• On the logarithmic connections over curves
• Area Estimates for High genus Lawson surfaces via DPW

Cited by in corpus (1)

• Constant mean curvature surfaces based on fundamental quadrilaterals