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arxiv: math/0302343 · v2 · submitted 2003-02-27 · 🧮 math.DG

Geometric inequalities on locally conformally flat manifolds

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keywords inequalityconformallyflatgeometriclocallymanifoldsassociatedconformal
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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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