报告名称：Non-extendability of complex structures

报告专家：彦文娇

专家所在单位：北京师范大学

报告时间：2025年12月11日 8:00-12:00

报告地点:  腾讯会议  646 876 525

专家简介：

彦文娇，入选国家级人才计划，现任北京师范大学数学学院教授、博士生导师、科研副院长。主要研究领域是微分几何，特别是等参超曲面、等参函数及其相关应用，代表性成果包括完全解决了等参情形的丘成桐第一特征值猜想、给出了Besse问题的一系列单连通例子等。主要研究成果均发表在J. Diff. Geom., Advances in Math., J. Funct. Anal., Comm. Anal. Geom., Sci. China Math., Math. Z., IMRN等国际高水平数学期刊上。

报告摘要：

Yau’s Problem 52 conjectures that every compact almost complex manifold of dimension ≥ 6 admits an integrable almost complex structure. Furthermore, Yau proposed a parabolic flow approach in the space of almost complex structures to deform an almost complex structure into an integrable one. In this talk, we establish the following result, which provides evidence that the deformation strategy envisioned in Yau’s Problem 52 is not applicable in certain natural geometric settings: On a specific open subset of the 6-dimensional sphere S^6, there exists a complex structure that can be extended to an almost complex structure on S^6, but cannot be extended to an integrable one. This talk is based on a joint work with Professor Zizhou Tang.