Application of the method of moving planes to conformally invariant equations

Mathematische Zeitschrift

Volumn 247, Issue 1, 2004, Pages 1-19

  Guan, Pengfei ^a   Lin, Chang Shou ^b   Wang, Guofang ^c  

^a MCMASTER UNIVERSITY   (Canada)

^b NATIONAL CHUNG CHENG UNIVERSITY   (Taiwan)

^c MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2442461129     PISSN: 00255874     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00209-003-0608-x     Document Type: Article

References (26)

1. Caffarelli, L., Nirenberg, L., Spruck, J.: The Dirichlet problem for nonlinear second-order elliptic equations. III. Functions of the eigenvalues of the Hessian. Acta Math. 155(3-4), 261-301 (1985)
2. Chang, S.Y.A., Gursky, M., Yang, P.: An equation of Monge-Ampere type in conformal geometry, and four-manifolds of positive Ricci curvature. Ann. Math. 155, 709-787 (2002)
3. Chang, S.Y.A., Gursky, M., Yang, P.: An a priori estimate for a fully nonlinear equation on four-manifolds. J. Anal. Math. 87, 151-186 (2002)
4. Chen, C.C., Lin, C.S.: Local Behavior of Singular Positive Solutions of Semilinear Elliptic Equations With Sobolev Exponent. Duke Math. J. 78, 315-334 (1995)
5. Chen, C.C., Lin, C.S.: Estimates of the conformal scalar curvature equation via the method of moving planes. Comm. Pure Appl. Math. 50, 971-1017 (1997)
6. Evans, L.C.: Classical solutions of fully nonlinear, convex, second-order elliptic equations. Comm. Pure Appl. Math. 35, 333-363 (1982)
7. Garding, L.: An inequality for hyperbolic polynomials. J. Math. Mech 8, 957-965 (1959)
8. Gidas, B., Ni, W.M., Nirenberg, L.: Symmetry and related properties via the maximum principle. Comm. Math. Phys. 68, 209-243 (1979)
9. Guan, P., Lin, C.S., Wang, G.: On quotient equations in conformal geometry. Preprint
10. Guan, P., Viaclovsky, J., Wang, G.: Some properties of the Schouten tensor and applications to conformal geometry. Trans. Am. Math. Soc. 355, 925-933 (2003)
11. Guan, P., Wang, G.: Local estimates for a class of fully nonlinear equations arising from conformal geometry. Intern. Math. Res. Notices 2003, 1413-1432 (2003)
12. Guan, P., Wang, G.: A fully nonlinear conformal flow on locally conformally flat manifolds. To appeer in J. Reine Angew. Math. 557, 219-238 (2003)
13. Guan, P., Wang, G.: Geometric inequalities on locally conformally flat manifolds. To appear in Duke Math. J.
14. Gursky, M.J.: Locally conformally flat four- and six-manifolds of positive scalar curvature and positive Euler characteristic. Indiana Univ. Math. J. 43, 747-774 (1994)
15. Gursky, M.J., Viaclovsky, J.: Fully nonlinear equations on Riemannian manifolds with negative curvature. Indiana Univ. Math. J. 52, 399-419 (2003)
16. Gursky, M.J., Viaclovsky, J.: A conformal invariant related to some fully nonlinear equations. To appear in Adv. in Math.
17. Gursky, M.J., Viaclovsky, J.: A fully nonlinear equation on 4-manifolds with positive scalar curvature. To appear in J. Diff. Geo.
18. Krylov, N.V.: Boundedly inhomogeneous elliptic and parabolic equation in a domain. Izv. Akad. Nauk SSSR 47, 75-108 (1983)
19. Li, A., Li, Y.Y.: On some conformally invariant fully nonlinear equations. Comm. Pure Appl. Math. 56, 1416-1464 (2003)
20. Li, A., Li, Y.Y.: A fully nonlinear version of the Yamabe problem and a Harnack type inequality. Preprint
21. Li, Y.Y.: Degree theory for second order nonlinear elliptic operators and its applications. Comm. Partial Differential Equations 14, 1541-1578 (1989)
22. Schoen, R.: On the number of constant scalar curvature metrics in a conformal class. Differential Geometry: A symposium in honor of Manfredo Do Carmo, H.B. Lawson and K. Tenenblat, (eds.), Wiley, 1991, pp. 311-32
23. Schoen, R., Yau, S.T.: Conformally flat manifolds, Kleinian groups and scalar curvature. Invent. Math. 92, 47-71 (1988)
24. Viaclovsky, J.: Conformal geometry, contact geometry, and the calculus of variations. Duke Math. J. 101, 283-316 (2000)
25. Viaclovsky, J.: Estimates and existence results for some fully nonlinear elliptic equations on Riemannian manifolds. Comm. Anal. Geom. 10, 815-847 (2002)
26. Viaclovsky, J.: Conformally invariant Monge-Ampere equations: global solutions. Trans. Am. Math. Soc. 352, 4371-4379 (2000)