Geometric inequalities on locally conformally flat manifolds
Pengfei Guan and Guofang Wang
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Submission date: 30. Sep. 2003
published in: Duke mathematical journal, 124 (2004) 1, p. 177-212
DOI number (of the published article): 10.1215/S0012-7094-04-12416-9
MSC-Numbers: 53C21, 35J60, 58E11
Keywords and phrases: sobolev inequality, quermassintegral inequality, moser-trudinger inequality, schouten tensor, fully nonlinear equation, conformal geometry
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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.