报告人： Hikaru Yamamoto (university of Tsukuba)

时间： 12月15日（周一）下午2:00-3:00

地点：清华大学数学系理科楼A404

题目：Critical norm blow-up for the harmonic map heat flow

摘要：A harmonic map heat flow admits a global (long-time) solution if the target manifold has nonpositive sectional curvature, by the classical theorem of Eells and Sampson. However, for general target manifolds without curvature assumptions, the flow may develop a singularity in finite time.In this talk, we focus on such finite-time blow-up and its characterization. At the maximal finite time, it is known that the "limsup" of the critical norm of the gradient of the map diverges to infinity. Recently, in joint work with Hideyuki Miura and Jin Takahashi, we proved that the "liminf" also diverges to infinity.