A regularity theorem for geometric equations (Q1568975)

The paper presents a regularity theorem for general parametric equations of curvature without using surface energies. The equation under consideration is \[ F(\Pi, \nu)=0, \] where \(\Pi\) is the second fundamental form of a surface \(S\) and \(\nu\) is its normal, \(F\) is assumed to be uniformly elliptic along the solution surface and Lipschitz in \(\nu\). The main result is that \(S\) is regular if it is ``flat enough''.