[This question][1] from Riemannian geometry:

> Consider a two-dimensional sphere with a Riemannian metric of total area $4\pi$. Does there exist a subset whose area equals $2\pi$ and whose boundary has length no greater than $2\pi$?

[1]: http://mathoverflow.net/questions/129773/isoperimetric-inequality-on-a-riemannian-sphere