常曲率空间中极小子流形的稳定性

Stability of Minimal Submanifold in Space of Constant Curvature

本文利用活动标架法与 Laplacian 的特征值方法研究了常曲率空间中极小子流形的稳定性.给出了常曲率空间中二维极小子流形的共形度量的高斯曲率之上界估计.证明了常曲率空间中二维极小子流形上一个单连通区域为稳定的充分条件.

This paper studies stability of minimal submanifold in space of constantcurvature by using moving frame method and eigenvalue method of the Lapla-cian.It gives the upper bound estimation of Gassian curvature of common formmeasure of 2—dimensional minimal submanifold in space of constant curvature.And it also proves a sufficient condition for a simple connected region withstability over 2—dimensional minimal submanifold in.space of constant curva-ture.