| 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. |
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