Title：Almost constancy of eigenfunctions of collapsing Einstein manifolds
Speaker：Shaosai Huang （University of Wisconsin-Madison）
Time：2019年7月26日 上午 10:00-11:00
Abstract：In 1987, Fukaya proved the continuity of eigenvalues of Riemannian manifolds with uniformly bounded curvature and diameter with respect to the measured Gromov-Hausdorff topology. With the major concern being a sequence of collapsing Riemannian manifolds, his result was based on a so-called key estimate, asserting that the eigenfunctions are almost constant along those collapsing directions. In this talk, we discuss a generalization of Fukaya's key lemma to the setting of collapsing Einstein manifolds, without assuming a uniform curvature bound.