報告題目： Lower Bounds for the First Eigenvalue of the Vibrating Clamped Plate under Compression
報告時間： 2015年 8月19日（周三）上午 10：00-11：00
報告地點： 中關村校區中心教學樓843（或844）教室

Abstract:   We give a sharp lower bound to the fundamental frequency of a clamped vibrating plate under compress in  the context of plates of different shapes of fixed area.  Mathematically, the problem is that of bounding the first eigenvalue of a certain 4th-order partial differential operator with leading term the bi-Laplacian from below by a positive constant over the square of the domain's area.  We give a Rayleigh-Faber-Krahn-type result for this problem.  (This is joint work with R. Benguria and R. Mahadevan.)  

報告人簡介： Professor Mark S. Ashbaugh 在Laplace的特征值及等周不等式方面做出了杰出的工作， 曾解決了著名的PPW猜想、二維及三維的Rayleigh猜想等。在《Annals of Mathematics》、《Bulletin of American mathematical Society》、《Duke Math. J.》、《Advances in Mathematics》、《Comm. Math. Phys.》等國際一流雜志上發表數十篇論文。