## On the motion of timelike minimal surfaces in the Minkowski space \$\textbf{R}^{1+n}\$    [PDF]

Weiping Yan
In this paper we are devoted to the study of the motion of the timelike minimal surfaces in the Minkowski space \$\textbf{R}^{1+n}\$. Those surfaces are known as membranes or relativistic strings, and described by a system with \$n\$ nonlinear wave equations of Born-Infeld type. We construct a global timelike Sobolev regularity torus in \$\textbf{R}^{1+n}\$, which time slice are evolved by a rigid motion. A Lyapunov-Schmidt decomposition reduces this problem to an infinite dimensional bifurcation equation and a range equation. To overcome the higher order derivative perturbation in bifurcation equation and the "small divisor" phenomenon in range equation, a suitable Nash-Moser iteration is constructed.
View original: http://arxiv.org/abs/1207.0368