| 摘要: |
| 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. |
| 关键词: 第一特征值 Hessian比较定理 子流形 平均曲率 |
| DOI： |
| 分类号:O186.12 |
| 基金项目:国家自然科学基金资助项目，西北师范大学重点学科(基础数学)基金 |
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| EIGENVALUES OF BOUNDED DOMAINS ON A MANIFOLD WITH NONPOSITIVE CURVATURE AND ITS SUBMANIFOLDS |
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LIU Jian-cheng,GUO Fang-cheng
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LIU Jian-cheng1,GUO Fang-cheng2(1.College of Math.and Info.Science,Northwest Normal University,Lanzhou 730070,China)(2.Dept.of Math.,Longdong University,Qingyang 745000,China)
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| Abstract: |
| 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. |
| Key words: first eigenvalue Hessian comparison theorem submanifold mean curvature |
