Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | Weiming Shen，Capital Normal University
| | Inviter: | | Title:
| Blow up sets of Ricci curvatures of complete conformal metrics | Time & Venue:
| 2021.06.04 15:40-16:30 N205 室 | 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.
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