题目：The Harmonic Heat Flow of Almost Complex Structures

报告人：Ph.D. He Weiyong （University of Oregon）

地点👍🏿🧑🏿‍🦳：zoom会议室

时间：2020年6月9日 10:00

Abstract. We define and study the harmonic heat flow for almost complex structures which are compatible with a Riemannian structure (M; g). This is a tensor-valued version of harmonic map heat flow. We prove that if the initial almost complex structure J has small energy(depending on the norm |/nabla J|), then the flow exists for all time and converges to a Kaehler structure. We also prove that there is a finite time singularity if the initial energy is sufficiently small but there is no Kaehler structure in the homotopy class. A main technical tool is a version of monotonicity formula, similar as in the theory of the harmonic map heat flow. We also construct an almost complex structure on a flat four tori with small energy such that the harmonic heat flow blows up at finite time with such an initial data.

Time: Tuesday, Jun 9, 2020 10:00 AM(Beijing)

Monday, Jun8, 2020 19:00 PM(Oregon, US)

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Meeting ID: 96578359208

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