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**, https://doi.org/10.1137/0120001**2.**R. Courant,*Methods of mathematical physics*. Vol. II:*Partial differential equations*, Interscience, New York, 1962. MR 25 # 4216.**3.**Herman Gluck,*The generalized Minkowski problem in differential geometry in the large*, Ann. of Math. (2)**96**(1972), 245–276. MR**309021**, https://doi.org/10.2307/1970788**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*, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 387–392. MR**0343207****6.**Jerry L. Kazdan and F. W. Warner,*Curvature functions for 2-manifolds*, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 387–392. MR**0343207****7.**Jerry L. Kazdan and F. W. Warner,*Curvature functions for 2-manifolds*, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 387–392. MR**0343207****8.**Jerry L. Kazdan and F. W. Warner,*Scalar curvature and conformal deformation of Riemannian structure*, J. Differential Geometry**10**(1975), 113–134. MR**365409****9.**Jerry L. Kazdan and F. W. Warner,*Remarks on some nonlinear elliptic equations*(to appear).**10.**M. A. Krasnosel′skiĭ,*Positive solutions of operator equations*, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron, P. Noordhoff Ltd. Groningen, 1964. MR**0181881****11.**J. Moser,*On a nonlinear problem in differential geometry*, Dynamical systems (Proc. Sympos., Univ. Bahia, Salvador, 1971) Academic Press, New York, 1973, pp. 273–280. MR**0339258****12.**D. H. Sattinger,*Monotone methods in nonlinear elliptic and parabolic boundary value problems*, Indiana Univ. Math. J.**21**(1971/72), 979–1000. MR**299921**, https://doi.org/10.1512/iumj.1972.21.21079**13.**R. Bruce Simpson and Donald S. Cohen,*Positive solutions of nonlinear elliptic eigenvalue problems*, J. Math. Mech.**19**(1969/70), 895–910. MR**0435566**

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