The evolution of the scalar curvature of a surface to a prescribed function

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1. [1] T. Aubin, Equations différentielles non linéaires et problème de Yamabe concernant la courbure scalaire, J.Math.Pures Appl. 55 (1976), 269-296. Zbl0336.53033MR431287
2. [2] T. Aubin, Meilleures constantes dans le théorème d’inclusion de Sobolev et un théorème de Fredholm non linéaire pour la transformation conforme de la courbure scalaire prescrite, J. Funct. Anal. 32 (1979), 148-174. Zbl0411.46019MR534672
3. [3] T. Aubin, Sur le problème de la courbure scalaire prescrite, Bull. Sci. Math. (5) 118 (1994), 465-474. Zbl0828.53035MR1305205
4. [4] J. Bartz – M. Struwe – R. Ye, A new approach to the Ricci flow on $S^2$, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 21 (1994), 475-482. Zbl0818.53050MR1310637
5. [5] S. Bismuth, Prescribed scalar curvature on a $C^{\infty }$ compact Riemannian manifold of dimension two, Bull. Sci. Math. 124 (2000), 239-248. Zbl0984.53017MR1753266
6. [6] S. Y. A. Chang – P. C. Yang, Prescribing Gaussian curvature on $S^2$, Acta Math. 159 (1987), 215-259. Zbl0636.53053MR908146
7. [7] S. Y. A. Chang – P. C. Yang, Conformal deformations of metric on $S^2$, J. Differential Geom. 27 (1988), 259-296. Zbl0649.53022MR925123
8. [8] S. Y. A. Chang – M. J. Gursky – P. C. Yang, The scalar curvature equation on 2- and 3-spheres, Calc. Var. Partial Differerential Equations 1 (1993), 205-229. Zbl0822.35043MR1261723
9. [9] W. Chen – C. Li, A note on Kazdan-Warner type conditions, J. Differential Geom. 41 (1995), 259-268. Zbl0822.53026MR1331968
10. [10] W. Chen – C. Li, A necessary and sufficient condition for the Nirenberg Problem, Comm. Pure Appl. Math. 47 (1995), 657-667. Zbl0830.35034MR1338474
11. [11] W. Chen – W. X. Ding, Scalar curvature on $S^2$, Trans. Amer. Math. Soc. 303 (1987), 365-382. Zbl0635.35026MR896027
12. [12] X. X. Chen, Calabi flows in Riemannian surfaces revisited; a new point of view, Int. Math. Res. Not. 6 (2001), 275-297. Zbl1078.53065MR1820328
13. [13] B. Chow, The Ricci-Hamilton flow on the 2-sphere, J. Differential Geom. 24 (1986), 153-179. 
14. [14] R. Hamilton, The Ricci flow on surfaces, Contemp. Math. 71 (1988), 237-262. Zbl0663.53031MR954419
15. [15] M. A. Jendoubi, A simple unified approach to some convergence Theorems of L.Simon, J. Funct. Anal. 153 (1998), 187-202. Zbl0895.35012MR1609269
16. [16] J. Kazdan – F. Warner, Curvature functions for compact 2-manifolds, Ann. of Math. 99 (1974), 14-47. Zbl0273.53034MR343205
17. [17] J. Kazdan – F. Warner, Existence and conformal deformation of metrics with prescribed Gaussian and scalar curvatures, Ann. of Math. 101 (1975), 317-331. Zbl0297.53020MR375153
18. [18] J. Moser, A sharp form of an inequality by N. Trudinger, Indiana Univ. Math. J. 20 (1971), 1077-1092. Zbl0213.13001MR301504
19. [19] J. Moser, On a nonlinear problem in differential geometry, In: “Dynamical systems” (M. Peixoto eds.), Academic Press, 1973. Zbl0275.53027MR339258
20. [20] E. Onofri, On the positivity of the effective action in a theory of random surfaces, Comm. Math. Physics 86 (1982), 321-326. Zbl0506.47031MR677001
21. [21] L. Simon, Asymptotics for a class of non-linear evolution equations, with applications to geometric problems, Ann. of Math. 118 (1983), 525-571. Zbl0549.35071MR727703
22. [22] M. Struwe, Curvature flows on surfaces, Ann. Scuola Norm. Sup. Pisa (5) 1 (2002), 247-274. Zbl1150.53025MR1991140
23. [23] X. Xu – P. Yang, Remarks on prescribing Gauss Curvature, Trans. Amer. Math. Soc. 336 (1993), 831-840. Zbl0823.53034MR1087058