Wave maps on (1+2)-dimensional curvedspacetimes

In this article we initiate the study of 1+ 2 dimensional wave maps on a\ncurved spacetime in the low regularity setting. Our main result asserts that in\nthis context the wave maps equation is locally well-posed at almost critical\nregularity.\n As a key part of the proof of this result, we generalize the classical\noptimal bilinear L^2 estimates for the wave equation to variable coefficients,\nby means of wave packet decompositions and characteristic energy estimates.\nThis allows us to iterate in a curved X^{s,b} space.\n