题目: Volume rigidity in Alexandrov geometry
星空（中国）人： Prof. Xiaochun Rong (Univ. of Rutgers, USA)
时间地点：光华东楼1704，2010/7/7 （周三）下午2：30--3：30

Abstract: We will report a recent progress in studying of volume
rigidity in Alexandrov geometry.
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题目: A geometric covering lemma and nodal sets of eigenfunctions
星空（中国）人：Prof.Guozhen Lu (Wayne State University, USA)
时间地点：光华楼1704，2010/7/7(周三）下午 3:30--4:30
Abstract: In this talk, we mainly present a geometric covering lemma which is akin to, but quite different from,  the classical Besicovitch covering lemma. This covering lemma is closely related to the growth property of eigenfunctions. As an application, we will sharpen some earlier estimates of Donnelly and C. Fefferman, Chanillo and Muckenhoupt, and Lu on the BMO norm estimates for the logarithm of eigenfunctions and lower bound of volume estimates of the nonzero sets of eigenfunctions on Riemannian manifolds. This is a joint work with Xiaolong Han.