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Aug 16, 2011 at 21:13 comment added Deane Yang Alas, although we do prove affine Sobolev inequalities, I don't offhand have any immediate answer for the question above. I don't see any obvious connection between the integral above and our affine invariant Sobolev "norms". If I find the time, I'll try to think about it more.
Aug 16, 2011 at 20:13 history answered Igor Rivin CC BY-SA 3.0