International Congress of Mathematicians

728 C. Thielealso in these degenerate cases; we will give examples below. This raises the questionwhether one can prove bounds on A uniformly in the choice of F, as F approachesone of these degenerate cases.Substantial progress on this question has only been made in the case dim(F) =1.Theorem 3.1 Let n > 3 and (ni, • • • ,n n ) be a unit vector spanning the space Y,and assume r\j ^ 0 for all j. Define the metricd(x,y) := supi