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On the elliptic equation \(\Delta \omega + K(x)e^{2\omega} = 0\) and conformal metrics with prescribed Gaussian curvatures. (English) Zbl 0487.35042


MSC:

35J60 Nonlinear elliptic equations
53C20 Global Riemannian geometry, including pinching
53C42 Differential geometry of immersions (minimal, prescribed curvature, tight, etc.)
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References:

[1] Kazdan, J.: Gaussian and scalar curvature, an update. In: Ann. Math. Studies Vol. 102 (S.-T. Yau, ed.). In press (1982) · Zbl 0481.53035
[2] Kazdan, J., Warner, F.W.: Curvature functions for compact 2-manifolds. Ann. Math.99, 14-47 (1974) · Zbl 0273.53034 · doi:10.2307/1971012
[3] Kazdan, J., Warner, F.W.: Curvature functions for open 2-manifolds. Ann. Math.99, 203-219 (1974) · Zbl 0278.53031 · doi:10.2307/1970898
[4] Ni. W.-M.: On the elliptic equation ?u+K(x)u n+2/n?2 =0. its generalizations and applications in geometry. Indiana Univ. Math. J. In Press (1982) · Zbl 0496.35036
[5] Noussair, E.S.: On the existence of solutions of nonlinear elliptic boundary value problems. J. Differential Equations34, 482-495 (1979) · Zbl 0435.35037 · doi:10.1016/0022-0396(79)90032-9
[6] Oleinik, O.A.: On the equation ?u+k(x)e u =0. Russian Math. Surveys33, 243-244 (1978) · Zbl 0401.35051 · doi:10.1070/RM1978v033n02ABEH002424
[7] Sattinger, D.H.: Conformal metrics in ?2 with prescribed curvature. Indiana Univ. Math. J.22. 1-4 (1972) · Zbl 0236.53009 · doi:10.1512/iumj.1972.22.22001
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