He would be able to patent all curved mirrors, just his particular implementation and design. He may have an optimal design that certainly would deserve patent protection.

The question that he has to worry about with the patents is whether or not his 2008 paper was published before or after the non-US patents were applied for. If I'm not mistaken, the US has a one year grace period between public display (publishing an academic paper) and filing for a patent. Whereas Europe et al. do not have a grace period.