Two examples are given of a sequence on a compact d-dimensional manifold (d ≥ 3) in a fixed conformal class satisfying a uniform L (d/2) bound on curvature and a bound on volume which are not compact in a C 0 topology. This shows that the curvature assumption of recent compactness results for conformal metrics is sharp.
All Science Journal Classification (ASJC) codes
- Geometry and Topology
- Conformal geometry
- Math Subject Classification: 53A30, 53C21
- compactness results