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Geometric inequalities on locally conformally flat manifolds
Pengfei Guan and Guofang WangAbstract
Through the study of some elliptic and parabolic fully nonlinear PDEs, we establish conformal versions of the quermassintegral inequality, the Sobolev inequality and the Moser-Trudinger inequality for the geometric quantities associated to the Schouten tensor on locally conformally flat manifolds.
- Received:
- 30.09.03
- Published:
- 30.09.03
- MSC Codes:
- 53C21, 35J60, 58E11
- Keywords:
- sobolev inequality, quermassintegral inequality, moser-trudinger inequality, schouten tensor, fully nonlinear equation, conformal geometry