摘要
By using a coupling technique,this paper presents some lower bounds of the first eigenvalue of an adjoint operator △+Z on compact M.This method is new and the proofs are straightforward.The method not only achieves the optimal bounds but also improves some known estimates Denote by g.d and D the Riemanman metric,dimension and diameter of M,respectively.Suppose that RicM≥-Kg for some real number K For the special case Z=0,the lower bound of A,provided by the paper am be summarized as followsBesides,a method of estimating the bound for general operators is given.Two examples,even on non-compact space,show that the estimates obtained by this method can be sharp.
By using a coupling technique,this paper presents some lower bounds of the first eigenvalue of an adjoint operator △+Z on compact M.This method is new and the proofs are straightforward.The method not only achieves the optimal bounds but also improves some known estimates Denote by g.d and D the Riemanman metric,dimension and diameter of M,respectively.Suppose that RicM≥-Kg for some real number K For the special case Z=0,the lower bound of A,provided by the paper am be summarized as followsBesides,a method of estimating the bound for general operators is given.Two examples,even on non-compact space,show that the estimates obtained by this method can be sharp.
基金
ProJect supported in part by the National Natural Science Foundation of China
State Eduction Commission of China
