11-27【Weiyong He】腾讯会议 GAP研讨班系列讲座之192


题目: Harmonic and biharmonic almost complex structures 

报告人:Weiyong He(University of Oregon) 

时间: 2020年1127, 周五,上午7:50-9:20  

地点:腾讯会议账号:950 391 9321 ; 密码112358

摘要:Harmonic almost complex structures was introduced by C. Wood in 1990s. We study the existence and regularity of weak harmonic almost complex structure from analytic point of view, as a tensor-valued version of harmonic maps. We introduce the notion of biharmonic almost complex structures, in particular in dimension four. We prove that biharmonic almost complex structures are smooth, and there always exist an energy-minimizing biharmonic almost complex structure. Moreover, given a homotopy class, we prove existence results which depends on whether M is spin or not. We also propose a conjecture that the homotopy class of energy-minimizing biharmonic almost complex structures do not depend on a generic background metric.