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Integrability conditions for \(\Delta u = k - Ke^{\alpha u}\) with applications to Riemannian geometry. (English) Zbl 0218.35030


MSC:

35J20 Variational methods for second-order elliptic equations
53A30 Conformal differential geometry (MSC2010)
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References:

[1] Melvyn S. Berger, On the conformal equivalence of compact 2-dimensional manifolds, J. Math. Mech. 19 (1969/1970), 13 – 18. · Zbl 0184.24904
[2] Melvyn S. Berger, Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds, J. Differential Geometry 5 (1971), 325 – 332. · Zbl 0222.53042
[3] Herman Gluck, Deformations of normal vector fields and the generalized Minkowski problem, Bull. Amer. Math. Soc. 77 (1971), 1106 – 1110. · Zbl 0227.53036
[4] Jerry L. Kazdan and F. W. Warner, Surfaces of revolution with monotonic increasing curvature and an application to the equation \Delta u = 1 - Ke, Proc. Amer. Math. Soc. (to appear). · Zbl 0228.53004
[5] Jerry L. Kazdan and F. W. Warner, The Trudinger inequality on manifolds (to appear). · Zbl 0261.53047
[6] Dimitri Koutroufiotis, Gaussian curvature and conformal mapping, J. Differential Geometry 7 (1972), 479 – 488. · Zbl 0268.53028
[7] J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1970/71), 1077 – 1092. · Zbl 0203.43701 · doi:10.1512/iumj.1971.20.20101
[8] Neil S. Trudinger, On imbeddings into Orlicz spaces and some applications, J. Math. Mech. 17 (1967), 473 – 483. · Zbl 0163.36402
[9] N. R. Wallach and F. W. Warner, Curvature forms for 2-manifolds, Proc. Amer. Math. Soc. 25 (1970), 712 – 713. · Zbl 0197.47901
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