一类偏微分方程的解的Bernstein性质

Bernstein Property for Solutions of a Partial Differential Equation

在局部严格凸的超曲面M上定义了α-相对度量G~α.研究了关于G~α完备且α-Ricci曲率有下界-N的超曲面M.利用活动标架法及J-C-P定理,证明了当ρ满足一个四阶偏微分方程时,M一定是椭圆抛物面.

A a-relative metric Ga was defined on a locally strongly convex hypersurface M. Let M be com- plete with respect to Ga and its a-Ricci curvature was hounded from below by a constant-N. By moving frames and J-C-P theorem, it drawed that the conclusion that M must be an elliptic paraboloid, when p satisfied a fourth order partial differential equation.