Radially symmetric wave maps from (1 + 2)-dimensional Minkowski space to the sphere

By a blow-up analysis as in 8] for a related problem we rule out concentration of energy for radially symmetric wave maps from the (1+ 2)-dimensional Minkowski space to the sphere. When combined with the local existence and regularity results of Christodoulou and Tahvildar-Zadeh for this problem, our result implies global existence of smooth solutions to the Cauchy problem for radially symmetric wave maps for smooth radially symmetric data. Received: 1 November 2000; in final form: 12 April 2001 / Published online: 1 February 2002