华东师范大学学报(自然科学版) ›› 2012, Vol. 2012 ›› Issue (4): 36-42.

• 数学 • 上一篇    下一篇

Ricci流下薛定谔方程的Harnack估计

王建红1,2   

  1. 1.黄山学院 数学系,黄山 245041; 2.华东师范大学 数学系,上海 200241
  • 收稿日期:2011-06-01 修回日期:2011-09-01 出版日期:2012-07-25 发布日期:2014-12-15

Harnack estimate for the Schrodinger equation under Ricci flow

WANG Jian-Hong 1,2   

  1. 1.Department of Mathematics, Huangshan University, Anhui 245041, China; 2.Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2011-06-01 Revised:2011-09-01 Online:2012-07-25 Published:2014-12-15

摘要: 利用C.M.Guenther处理热方程的方法证明了,度量沿Ricci流演化的闭流形上薛定谔方程正解的梯度估计和Harnack不等式,从而推广了有关结论.

关键词: 薛定谔方程, 梯度估计, Harnack不等式, Ricci流

Abstract: This paper established the gradient estimate and Harnack inequalities of the Schrodinger equation when the metric is evolved by Ricci flow, and extended the results ofthe heat equation by C.M.Guenther

Key words: Schrodinger equation, gradient estimate, Harnack inequalities, Ricci flow

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