Title: Analysis of measures converging to a Dirac-delta measure in Riemann surfaces

Date: 02/27/2019

Time: 4:10 PM - 5:00 PM

Place: C304 Wells Hall

This is a 2-dim case of general energy concentration phenomenon. If we have sequence of harmonic maps with bounded energy defined on a Riemann surface, Uhlenbeck compactness theorem says its subsequence converges away from at most finite points, called bubble points. At the bubble point energy concentrates, so we may blow up the point to capture energy distribution on the bubble. But energy may concentrate again on the bubble, so careful touch is needed to finish this blow up process. In this talk I will introduce a way to choose two marked points with desired properties. The typical example is of harmonic map case, but it may be applied to other energy concentrating cases.