Special Session 123: New trends in elliptic and parabolic PDEs

Conformal metrics of constant scalar curvature with unbounded volumes

Liuwei Gong
The Chinese University of Hong Kong
Hong Kong
Co-Author(s):    Yanyan Li
Abstract:
When $n>24$, Brendle and Marques constructed a smooth metric on $S^n$ such that there exists a sequence of conformal metrics with the same positive constant scalar curvature but with unbounded Ricci curvatures. We find a ``worse`` blowup phenomenon when $n>24$: a smooth metric on $S^n$ such that there exists a sequence of conformal metrics with the same positive constant scalar curvature but with unbounded volumes (and, in particular, unbounded Ricci curvatures). This is a joint work with Yanyan Li.