1207.0368 (Weiping Yan)

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