News icon 学术报告
Gywm line


时间:2015年1月16日(周五) 上午8:30-9:30
题目:On sharp lower bound of the spectral gap for a Schrodinger operator and some related results
报告人:何跃 副教授(南京师范大学)
摘要: In this talk, we give an easy proof of the main results of Andrews and Clutterbuck's paper [Proof of the fundamental gap conjecture, J. Amer. Math. Soc. 24 (2011), no. 3, 899--916] which gives both a sharp lower bound for the spectral gap of a Schrodinger operator and a sharp modulus of concavity for the logarithm of the corresponding first eigenfunction. We arrive directly at same estimates by the `double coordinate' approach and asymptotic behavior of parabolic flows. Although using the techniques appeared in the above paper, we partly simplify the method and argument. This may help to provide an easy way for estimating spectral gap. Besides, we also get a new lower bound of spectral gap for a class of Schrodinger operator.

时间:2015年1月16日(周五) 上午9:40-11:40
报告人:Pak Tung Ho 副教授(Sogang University, Korea)
摘要: I will talk about the definition of Q-curvature and some of its properties. Then I will talk about the problem of prescribing Q-curvature, especially I will explain the ideas of studying the problem using flow approach.