UNCOUNTABLY MANY C-0 CONFORMALLY DISTINCT LORENTZ SURFACES AND A FINITENESS THEOREM

This paper describes an uncountable family of Lorentz surfaces realize d as rectangular regions in the Minkowski 2-plane E(1)(2). A Simple C- 0 conformal invariant is defined which assigns a different real value to each Lorentz surface in the family. While these surfaces provide un countably many C-0 conformally distinct, bounded, convex subsets of E( 1)(2) which are each symmetric about a properly embedded timelike curv e and about a properly embedded spacelike curve, it is shown that ther e are only 21 C-0 conformally distinct, bounded, convex subsets of E(1 )(2) which are symmetric about some null liner.