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科学研究
报告题目:

Blow up sets of Ricci curvatures of complete conformal metrics

报告人:

沈伟明 副教授 (首都师范大学)

报告时间:

报告地点:

腾讯会议 ID:972 454 652

报告摘要:

A version of the singular Yamabe problem in bounded domains yields complete conformal metricswith negative constant scalar curvatures. In this talk, we will talk about blow-up phenomena of Ricci curvatures of these metrics on domains whose boundary is close to certain limit set of a lower dimension. We will characterize the blow-up set according to theYamabe invariant of the underlying manifold. In particular, we will prove that all points in the lower dimension part of the limit set belong to the blow-up set on manifolds not conformally equivalent to the standard sphere and that all but one point in the lower dimension part of the limit set belong to the blow-up set on manifolds conformally equivalent to the standard sphere. We will demonstrate by examples that these results are optimal.

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