Abstract: We prove that the regularity of the extremal function of a compact subset of a compact Kahler manifold is a local property, and that the continuity and Holder continuity are equivalent to classical notions of the local L-regularity and the locally Holder continuous property in pluripolential theory. As a consequence we give an effective characterization of the (C^{\alpha},C^{\alpha'})-regularity of compact sets, the notion introduced by Dinh, Ma and Nguyen. Using this criterion all compact fat subanalytic subsets in R^n are shown to be regular in this sense.

Bio-Sketch: Ngoc Cuong Nguyen is currently an assistant professor at KAIST (Korea Advanced Institute of Science and Technology). He obtained his Ph.D. at Jagiellonian University in 2014 under the supervision of Slawomir Kolodziej. His research focuses on pluripotential theory, geometric analysis and complex dynamic in higher dimension.

Zoom: https://us02web.zoom.us/j/84438146451?pwd=NHAwLy9VNHhFRWRJV0VqNzgrdSthQT09                                                                        Meeting ID: 844 3814 6451    Passcode: 150000