Application of The Method of Moving Planes to Conformally Invariant Equations
Pengfei Guan, Chang-Shou Lin, and Guofang Wang
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Submission date: 25. Nov. 2003
published in: Mathematische Zeitschrift, 247 (2004) 1, p. 1-19
DOI number (of the published article): 10.1007/s00209-003-0608-x
MSC-Numbers: 53C21, 35J60, 58E11
Keywords and phrases: moving plane method, harnack inequality, fully nonlinear equation, locally conformally flat, sphere theorem
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In this paper, we apply the method of moving planes to a class of fully nonlinear conformal equations on locally conformally flat manifolds. The Harnack inequality, global estimates and hence existence are obtained for solutions. As an application, we obtain a sphere theorem.