## Sectors with Density in Granada

My undergraduate research Geometry Group and I have been having a great summer here in Granada Spain. We’ve been considering planar sectors of angle with density and the isoperimetric problem: to enclose given weighted area with least weighted perimeter. We’ve proved that there are angles such that the minimizer is:

1. for , a circular arc about the origin;

2. for , an unduloid (half-period of a periodic curve normal to both edges of the sector);

3. for , a semicircle through the origin.

We have lots of evidence that and , but we have not been able to prove it. Can you help us? Check out our arXiv post.