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Analysis Seminar

Thursday, April 13, 2017 - 3:00pm

Dennis Kriventsov

New York University


University of Pennsylvania


A classical problem in analysis is to relate information about the spectrum of the Laplacian of a domain to that domain's shape. One approach to this program is by studying sets which minimize some function of their Laplacian's eigenvalues, with, say, a volume constraint. I will explain how to study the local structure of the boundaries of such minimizers by interpreting the configuration as a vector-valued free boundary problem. Then I will present some new regularity results for these free boundaries. This is based on joint work with Fanghua Lin.