Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	沈伟明
Inviter:	简旺键
Title:	Blow up sets of Ricci curvatures of complete conformal metrics
Language:	Chinese
Time & Venue:	2023.12.29 10:00-11:00 腾讯会议：866-1301-8136
Abstract:	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.