Integrability conditions for $\Delta u = k - Ke^{\alpha u}$ with applications to Riemannian geometry

Authors:
Jerry L. Kazdan and F. W. Warner

Journal:
Bull. Amer. Math. Soc. **77** (1971), 819-823

MSC (1970):
Primary 35J20, 35J60, 53A30, 53C20; Secondary 53C45

MathSciNet review:
0282314

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References | Similar Articles | Additional Information

**1.**Melvyn S. Berger,*On the conformal equivalence of compact 2-dimensional manifolds*, J. Math. Mech.**19**(1969/1970), 13–18. MR**0244906****2.**Melvyn S. Berger,*Riemannian structures of prescribed Gaussian curvature for compact 2-manifolds*, J. Differential Geometry**5**(1971), 325–332. MR**0295261****3.**Herman Gluck,*Deformations of normal vector fields and the generalized Minkowski problem*, Bull. Amer. Math. Soc.**77**(1971), 1106–1110. MR**0284955**, 10.1090/S0002-9904-1971-12885-9**4.**Jerry L. Kazdan and F. W. Warner,*Surfaces of revolution with monotonic increasing curvature and an application to the equation*∆*u*= 1 —*Ke*, Proc. Amer. Math. Soc. (to appear).**5.**Jerry L. Kazdan and F. W. Warner,*The Trudinger inequality on manifolds*(to appear).**6.**Dimitri Koutroufiotis,*Gaussian curvature and conformal mapping*, J. Differential Geometry**7**(1972), 479–488. MR**0328835****7.**J. Moser,*A sharp form of an inequality by N. Trudinger*, Indiana Univ. Math. J.**20**(1970/71), 1077–1092. MR**0301504****8.**Neil S. Trudinger,*On imbeddings into Orlicz spaces and some applications*, J. Math. Mech.**17**(1967), 473–483. MR**0216286****9.**N. R. Wallach and F. W. Warner,*Curvature forms for 2-manifolds*, Proc. Amer. Math. Soc.**25**(1970), 712–713. MR**0262976**, 10.1090/S0002-9939-1970-0262976-6

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DOI:
https://doi.org/10.1090/S0002-9904-1971-12818-5