Caps on Hermitian varieties and maximal curves

A lower bound for the size of a complete cap of the polar space H(n,q²) associated to the non-degenerate Hermitian variety Un is given; this turns out to be sharp for even q when n=3. Also, a family of caps of H(n,q²) is constructed from Fq²-maximal curves. Such caps are complete for q even, but not necessarily for q odd.