非正曲率流形及其子流形上有界区域的特征值

EIGENVALUES OF BOUNDED DOMAINS ON A MANIFOLD WITH NONPOSITIVE CURVATURE AND ITS SUBMANIFOLDS

本文研究了完备单连通具有非正曲率黎曼流形及其子流形上有界区域的特征值问题.利用广义Hessian比较定理,获得了局部特征值的下界估计式,将McKean[2]的定理在局部上推广到了非正曲率的情形.

In this article,we study the first eigenvalue problems on complete simply connected Riemannian manifold with nonpositive sectional curvatures and its submanifolds with bounded mean curvature.By using generalized Hessian comparison theorem,we obtain a local bound from below of the first eigenvalue,and generalize the results in [2] due to H.P.McKean locally to the case of manifolds with nonpositive sectional curvatures.