FINSLER流形上局部LIPSCHITZ函数的变分

VARIATION OF LOCALLY LIPSCHITZ FUNCTION ON FINSLER MANIFOLD

本文把Banach空间的局部Lipchitz函数的Clarke广义梯度理论推广到Finsler流形的情形,并讨论了相应的局部Lipschitz函数的变分性质,包括伪梯度向量场,形变引理,Morse不等式。

In this paper, we generalize the generalized gradient of clarke on Banach manifold to the case of Finsler manifold and discuss the variational property of corresponding locally Lipschitz function, such as pseudo-gradient vector field, deformation lemma and Morse inequality.