Title: Scalar curvature flow on $S^n$---perturbation theorem revisited

Speaker: 陈学长（北京大学）

Time: May 19, 2011, 2:00-4:00 pm

Venue: Room 1328 at BICMR, Resource Plaza, Peking University

Abstract: This talk is based on our recent joint work with Prof. Xu Xingwang at NUS.
Using a negative energy gradient flow, we reconsidered the perturbation theorem of prescribing scalar curvature problem on $S^n$(A. Chang & P. Yang, Duke Math. J. 64 (1991), 27-69).
Our main result is as follows: suppose
(i) $f$ is a smooth positive Morse function with non-degeneracy;
(ii) simple bubble condition (abbr. (sbc)) of $f$;
(iii) some topological condition, such as degree condition or index-counting condition or even slightly weaker condition; then the candidate function $f$ can be realized as the scalar curvature of some conformal metric to the standard metric on the sphere. However, in present stage, the condition (sbc) is crucial to our analysis in this flow approach.