A logarithmic Gauss curvature flow and the Minkowski problem
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 6, pp. 733-751. 
@article{AIHPC_2000__17_6_733_0,
     author = {Chou, Kai-Seng and Wang, Xu-Jia},
     title = {A logarithmic {Gauss} curvature flow and the {Minkowski} problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {733--751},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {6},
     year = {2000},
     mrnumber = {1804653},
     zbl = {01558333},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2000__17_6_733_0/}
}
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Chou, Kai-Seng; Wang, Xu-Jia. A logarithmic Gauss curvature flow and the Minkowski problem. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 6, pp. 733-751. http://archive.numdam.org/item/AIHPC_2000__17_6_733_0/

[1] Andrews B., Contraction of convex hypersurfaces by their affine normal, J. Differential Geom. 43 (1996) 207-229. | MR | Zbl

[2] Andrews B., Evolving convex curves, Calc. Var. PDE 1 (1998) 315-371. | MR | Zbl

[3] Cheng S.Y., Yau S.T., On the regularity of the solution of the n-dimensional Minkowski problem, Comm. Pure Appl. Math. 29 (1976) 495-516. | MR | Zbl

[4] Chou K. (Tso, K.), Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure Appl. Math 38 (1985) 867-882. | MR | Zbl

[5] Chou K. (Tso, K.), Convex hypersurfaces with prescribed Gauss-Kronecker curvature, J. Differential Geom. 34 (1991) 389-410. | MR | Zbl

[6] Chou K., Zhu X., Anisotropic curvature flows for plane curves, Duke Math. J. 97 (1999) 579-619. | MR | Zbl

[7] Chow B., Deforming convex hypersurfaces by the n-th root of the Gaussian curvature, J. Differential Geom. 22 (1985) 117-138. | MR | Zbl

[8] Firey W., Shapes of worn stones, Mathematica 21 (1974) 1-11. | MR | Zbl

[9] Gage M.E., Li Y., Evolving plane curves by curvature in relative geometries II, Duke Math. J. 75 (1994) 79-98. | MR | Zbl

[10] Gerhardt C., Flow of non convex hypersurfaces into spheres, J. Differential Geom. 32 (1990) 299-314. | Zbl

[11] Krylov N.V., Nonlinear Elliptic and Parabolic Equations of the Second Order, D. Reidel, 1987. | MR | Zbl

[12] Lewy H., On differential geometry in the large, I (Minkowski's problem), Trans. Amer. Math. Soc. 43 (1938) 258-270. | JFM | MR | Zbl

[13] Minkowski H., Allgemeine Lehrsätze über die konvexen Polyeder, Nachr. Ges. Wiss. Göttingen (1897) 198-219. | EuDML | JFM

[14] Minkowski H., Volumen and Oberfläche, Math. Ann. 57 (1903) 447-495. | EuDML | JFM | MR

[15] Miranda C., Su un problema di Minkowski, Rend. Sem. Mat. Roma 3 (1939) 96- 108. | JFM | MR | Zbl

[16] Nirenberg L., The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953) 337-394. | MR | Zbl

[17] Pogorelov A.V., The Multidimensional Minkowski Problem, J. Wiley, New York, 1978.

[18] Urbas J.I.E., On the expansion of convex hypersurfaces by symmetric functions of their principal radii of curvature, J. Differential Geom. 33 (1991) 91-125. | MR | Zbl