Geometric inequalities on locally conformally flat manifolds

Details Geometric inequalities on locally conformally flat manifolds Geometric inequalities on locally conformally flat manifolds

2003-02-27

arxiv.org/abs/math/0302343v2

Mathematics

Differential Geometry

30 pages. Final version, accepted by Duke Math. J

Scientific paper

Through the study of some elliptic and parabolic fully nonlinear PDEs, we
establish conformal versions of quermassintegral inequality, the Sobolev
inequality and the Moser-Trudinger inequality for the geometric quantities
associated to the Schouten tensor on locally conformally flat manifolds.

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