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Haha just reading it raises an old memory.
An old friend in the 1970's tried exactly the same thing, using very thin circular glass disks which were cut from old plates from the UK48" schmidt at Siding Spring, then aluminised. They were perhaps 2-3 mm thick and of pretty reasonable optical quality in terms of flatness etc..
After making a rather magnificent assembly of two large rings with about 40 caps screws to gently apply pressure around the permitter of the plate, he was rather disappointed to find the resulting concave mirror wouldn't form a decent image.
At the time I was studying maths and was able to solve for the shape of the surface - its a nasty shape not even close to spherical, let alone parabolic.
Reading the abstract suggests this fellow has tried to do the same.
He then went on to try sealing the plate against the ring using an O-ring, and using a partial vacuum behind to deform the plate. This also produces a concave mirror (better than the first attempt) however still nowhere near good enough for anything much, from memory the figure this produces is some sort of quartic.
Just goes to show who does - and doesn't understand what a paraboloid is (or isn't) and how accurate it must be to produce a decent image.
Lastly, I am surprised he was awarded a patent for this as there is plenty of "prior art" on this topic in mathematics circles - its a classic 2nd year differential equation problem in Applied Maths. It seems lately that the US Patent office will issue a patent for anything on the basis of "wait and see" with the expectation someone else may challenge the patent in court, rather that attempting to do any serious searches or critical research first.
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