What is the Pompeiu problem and is it related to Navier-Stokes?

[greentea28a]

Hi,
http://en.wikipedia.org/wiki/Pompeiu_problem

Can someone rephrase the problem so I better understand its meaning?

And has it been solved? Solution to Pompeiu Problem http://arxiv.org/abs/1304.2297

Thanks

PS. does this problem have anything to do with Navier-Stokes?

 

[johnqwertyful]

What's your background?