应用数学2011，Vol.24Issue(2)：274-278,5.
Yamabe流下Laplace算子的第一特征值
The First Eigenvalue of the Laplace Operator under Yamabe Flow
摘要
Abstract
In this paper,we derive the evolution equation for the first eigenvalue of Laplace operator along Yamabe flow.We prove that on the smooth homogeneous manifold (Mn,g0),if λ(t) denotes the first eigenvalue of Laplace operator,then under normalized Yamabe flow,we have λ =d,and we can also get under the unnormalized Yamabe flow,λ(t) =ded,where c is the scalar curvature of smooth homogeneous manifold and d is a constant.Moreover,as applications,we construct some monotonic quantities under this flow.关键词
拉普拉斯/Yamabe流/特征值/单调性Key words
Laplace operator/Yamabe flow/Eigenvalue/Monotonicity分类
数理科学引用本文复制引用
赵亮..Yamabe流下Laplace算子的第一特征值[J].应用数学,2011,24(2):274-278,5.基金项目
Foundation item:Supported by the School Foundation (1008-56YAH10030) and the Youth Foundation of China (11001115) （1008-56YAH10030）
