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| A NEW LAPLACIAN COMPARISON THEOREM AND THE ESTIMATE OF EIGENVALUES |
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Citation： |
Ding Qing.A NEW LAPLACIAN COMPARISON THEOREM AND THE ESTIMATE OF EIGENVALUES[J].Chinese Annals of Mathematics B,1994,15(1):35~42 |
| Page view： 1338
Net amount： 782 |
Authors： |
Ding Qing; |
Foundation： |
Project supported partially by the Science Foundation
of State Education Commission and the National Natural Science Foundation of China |
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| Abstract： |
This paper establishes a new Laplacian comparison
theorem which is specially useful to the manifolds of nonpositive curvature.
It leads naturally to the corresponding
heat kernel comparison and eigenvalue comparison theorems. Furthermore, a
lower estimate of $L^2$-spectrum of an $n$-dimensional non-compact complete Cartan-Hadamard
manifold is given by $(n-1)k/4$, provided its Ricci curvature $\le-(n-1)k$
$(k=\roman {const.}\ge 0)$. |
Keywords： |
Laplacian operator, Comparison theorem, Heat kernel, Eigenvalue. |
Classification： |
53C21,58G25 |
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