题目: On sharp lower bound of the spectral gap for a Schr/"odinger operator and some related results

报告人：何跃（南京师范大学）

时间: 2014年12月22日, 周一   下午15:00-16:30

地点：管理楼1611

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 Schr/"odinger 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 maybe 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 Sch/"odinger operator.

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