Curvature functions for 2-manifolds with negative Euler characteristic

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

Journal:
Bull. Amer. Math. Soc. **78** (1972), 570-574

MSC (1970):
Primary 35J25, 35J60, 53A90, 53C99; Secondary 35R05, 58G99, 47H15, 53C20

DOI:
https://doi.org/10.1090/S0002-9904-1972-13006-4

MathSciNet review:
0320947

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References | Similar Articles | Additional Information

**1.**Donald S. Cohen,*Multiple stable solutions of nonlinear boundary value problems arising in chemical reactor theory*, SIAM J. Appl. Math. 20 (1971), 1-13. MR**274848****2.**R. Courant,*Methods of mathematical physics*. Vol. II:*Partial differential equations*, Interscience, New York, 1962. MR 25 # 4216.**3.**H. Gluck,*The generalized Minkowski problem in differential geometry in the large*, Ann. of Math, (to appear). MR**309021****4.**Jerry L. Kazdan and F. W. Warner,*Integrability conditions for Δu = k - Ke*, Bull. Amer. Math. Soc. 77 (1971), 819-823.**5.**Jerry L. Kazdan and F. W. Warner,*Curvature functions for*2 -*manifolds*. I (to appear). MR**343207****6.**Jerry L. Kazdan and F. W. Warner,*Curvature functions for*2 -*manifolds*. II (to appear). MR**343207****7.**Jerry L. Kazdan and F. W. Warner,*Curvature functions for*2 -*manifolds*. III.*The negative Euler characteristic case*(to appear). MR**343207****8.**Jerry L. Kazdan and F. W. Warner,*Scalar curvature and conformal deformation of Riemannian structure*(to appear). MR**365409****9.**Jerry L. Kazdan and F. W. Warner,*Remarks on some nonlinear elliptic equations*(to appear).**10.**M. A. Krasnoselskiĭ,*Positive solutions of operator equations*, P. Noordhoff Ltd., 1964 (translated from the 1960 Russian edition), see especially Chapter 4. MR**181881****11.**J. Moser,*On a nonlinear problem in differential geometry*(to appear). MR**339258****12.**D. H. Sattinger,*Monotone methods in nonlinear elliptic and parabolic boundary value problems*(to appear). MR**299921****13.**R. B. Simpson and Donald S. Cohen,*Positive solutions of nonlinear elliptic eigenvalue problems, J*. Math. Mech. 19 (1970), 895-910. MR**435566**

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DOI:
https://doi.org/10.1090/S0002-9904-1972-13006-4