Lawson CMC Surfaces

Nicholas Schmitt

Description


In 1970, Herbert Blaine Lawson gave a description of complete minimal surfaces in $S^3$ [1]. For visualization one can use the stereographic projection to $\mathbb{R}^3$ as for instance is seen here. The resulting surfaces are known to be CMC-surface in euclidean 3-space. One can obtain Lawson surfaces by solving a Plateau problem on a spherical geodesic quadrilateral followed by suitable reflections.

We have images of:
- The Lawson minimal surfaces $\xi_{g,1}$ in various stereographic projections.
- A Lawson CMC surface with six lobes
- The Lawson minimal surface $\xi_{g,1}$ of genus 2 with curvature lines rotated to closed curvature lines with rational slope
- The family 0 of Lawson symmetric constant mean curvature surfaces of genus 2.
- The family 1 of Lawson symmetric constant mean curvature surfaces of genus 2.

Supplement materials


References


  1. [1] Herbert B. Lawson. Complete minimal surfaces in $S^3$. The Annals of Mathematics, 1970. URL: http://www.math.jhu.edu/~js/Math748/lawson.s3.pdf.

Dr. Nicholas Schmitt   +

University: TU Berlin
Website: http://page.math.tu-berlin.de/~schmitt/