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

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

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 (1969/70), 13-18. MR 39 #6219. MR**244906****2.**Melvyn S. Berger,*On Riemannian structures of prescribed Gauss curvature for compact two-dimensional manifolds*, J. Differential Geometry 5 (1971) (to appear). MR**295261****3.**Herman Gluck,*Deformations of normal vector fields and the generalized Minkowski problems*, Bull. Amer. Math. Soc. 77 (1971) (to appear). MR**284955****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.**D. Koutroufiotis,*On Gaussian curvature and conformal mapping*(to appear). MR**328835****7.**J. Moser,*A sharp form of an inequality by N. Trudinger*, Indiana Univ. Math. J. 20 (1971) (to appear). MR**301504****8.**Neil S. Trudinger,*On imbeddings into Orlicz spaces and some applications*, J. Math. Mech. 17 (1967), 473-483. MR 35 #7121. MR**216286****9.**N. Wallach and F. W. Warner,*Curvature forms for 2-manifolds*, Proc. Amer. Math. Soc. 25 (1970), 712-713. MR**262976**

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