Survey on the parabolic kernel of the Schrödinger operator

Survey on the parabolic kernel of the Schrödinger operator

陳敬佳(Jing-Jia Chen)

指導教授 ： 徐淑裕

國立中正大學/理學院/數學系研究所/碩士(2016年)

摘要

這篇論文再探討 On the parabolic kernel of the Schrödinger operator.

關鍵字

熱傳導方程式 ； 黎曼流形

並列摘要

In this thesis I will survey the paper ”on the parabolic kernel of the Schrödinger operator” by P.Li and S.T.Yau

並列關鍵字

heat equation ； heat kernel ； parabolic equation ； upper bounded ； lower bounded

參考文獻

[1] Aronson, D. G., Uniqueness of positive weak solutions of second order

parabolic equations, Ann. Polon. Math., 16 (1965), 285-303.

[2] Azencott, R., Behavior of diffusion semi-groups at infinity, Bull. Soc.

kernel estimates for functions of the Laplace operator, and the geometry of complete

Riemannian manifolds. J. Differential Geom., 17 (1983), 15-33.