Flow through Lawson Surfaces

Nicholas Schmitt

Description

The Lawson surfaces $\xi_{p,q}$ are a family of minimal surfaces in $S^3$ of genus $pq$. There is a flow through minimal surface in which the two integers are replaced by real parameters.
Shown in the images is one leg of this flow, e.g. from the Lawson surface $\xi_{2,1}$ of genus 2 to $\xi_{2,2}$ of genus 4. An order 2 symmetry of the initial surface with six fixed points is “opened” along three cuts until it reaches an order 3 symmetry. The final surface is show before and after the missing piece is filled in.

Also a flow from the Clifford torus $\xi_{1,1}$ of genus 1 to the Lawson minimal surfaces $\xi_{1,2}$ of genus 2 can be seen. Note, that the flow breaks the topology. Moreover, flows from a Delaunay torus to a Lawson CMC surface of genus 2 are shown.

References

Dr. Nicholas Schmitt   +

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