Geodesic
The evolution of the scalar curvature of a surface to a prescribed function
Baird, Paul1  ; Fardoun, Ali1  ; Regbaoui, Rachid1 
1 Département de Mathématiques Université de Brest 6, Avenue Le Gorgeu 29285 Brest, France
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 1, pp. 17-38

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We investigate the gradient flow associated to the prescribed scalar curvature problem on compact riemannian surfaces. We prove the global existence and the convergence at infinity of this flow under sufficient conditions on the prescribed function, which we suppose just continuous. In particular, this gives a uniform approach to solve the prescribed scalar curvature problem for general compact surfaces.

Classification : 58E20

Baird, Paul 1 ; Fardoun, Ali 1 ; Regbaoui, Rachid 1

1 Département de Mathématiques Université de Brest 6, Avenue Le Gorgeu 29285 Brest, France 
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     title = {The evolution of the scalar curvature of a surface to a prescribed function},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {17--38},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {1},
     year = {2004},
     mrnumber = {2064965},
     zbl = {1170.58306},
     language = {en},
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Baird, Paul; Fardoun, Ali; Regbaoui, Rachid. The evolution of the scalar curvature of a surface to a prescribed function. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 1, pp. 17-38. http://geodesic.mathdoc.fr/item/ASNSP_2004_5_3_1_17_0/