PIMS - SFU Discrete Math Seminar: Yifan Jing
Topic
Minimal and Nearly Minimal Measure Expansions in Locally Compact Groups
Speakers
Details
Abstract: In 1964, Kemperman proved the following continuous nonabelian counterpart of the Cauchy-Davenport theorem: If G is a connected unimodular locally compact group with a left (and hence right) Haar measure \mu, A, B \subseteq G are nonempty and compact, and AB is their product set, then
\mu(AB) \geq \min\{ \mu(A) + \mu(B), \mu(G)\}.
I will present the recent joint works with Jinpeng An, Chieu-Minh Tran and Ruixiang Zhang where we determine the conditions for the equality to happen or nearly happen in the above inequality. Our results and methods answer several questions by Griesmer, Henstock, Hrushovski, Kemperman, Macbeath, McCrudden, and Tao.