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Questions about partial differential equations of hyperbolic type. Often used in combination with the top-level tag ap.analysis-of-pdes.

4 votes

Upper bound on the number of convex connected components of the complement of the zero set o...

It may be that the bound is only fairly good for $r \ll n.$ This is supported by the following which is an elaboration on the comment by Boris Bukh. We can get a lower bound of $$ f(r,n)=\sum_{j=0} …
Aaron Meyerowitz's user avatar