A logarithmic Gauss curvature flow and the Minkowski problem
Annales de l'I.H.P. Analyse non linéaire, Volume 17 (2000) no. 6, p. 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},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {6},
     year = {2000},
     pages = {733-751},
     zbl = {01558333},
     mrnumber = {1804653},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2000__17_6_733_0}
}
Chou, Kai-Seng; Wang, Xu-Jia. A logarithmic Gauss curvature flow and the Minkowski problem. Annales de l'I.H.P. Analyse non linéaire, Volume 17 (2000) no. 6, pp. 733-751. http://www.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 1424425 | Zbl 0858.53005

[2] Andrews B., Evolving convex curves, Calc. Var. PDE 1 (1998) 315-371. | MR 1660843 | Zbl 0931.53030

[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 423267 | Zbl 0363.53030

[4] Chou K. (Tso, K.), Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure Appl. Math 38 (1985) 867-882. | MR 812353 | Zbl 0612.53005

[5] Chou K. (Tso, K.), Convex hypersurfaces with prescribed Gauss-Kronecker curvature, J. Differential Geom. 34 (1991) 389-410. | MR 1131436 | Zbl 0723.53041

[6] Chou K., Zhu X., Anisotropic curvature flows for plane curves, Duke Math. J. 97 (1999) 579-619. | MR 1682990 | Zbl 0946.53033

[7] Chow B., Deforming convex hypersurfaces by the n-th root of the Gaussian curvature, J. Differential Geom. 22 (1985) 117-138. | MR 826427 | Zbl 0589.53005

[8] Firey W., Shapes of worn stones, Mathematica 21 (1974) 1-11. | MR 362045 | Zbl 0311.52003

[9] Gage M.E., Li Y., Evolving plane curves by curvature in relative geometries II, Duke Math. J. 75 (1994) 79-98. | MR 1284816 | Zbl 0811.53033

[10] Gerhardt C., Flow of non convex hypersurfaces into spheres, J. Differential Geom. 32 (1990) 299-314. | Zbl 0708.53045

[11] Krylov N.V., Nonlinear Elliptic and Parabolic Equations of the Second Order, D. Reidel, 1987. | MR 901759 | Zbl 0619.35004

[12] Lewy H., On differential geometry in the large, I (Minkowski's problem), Trans. Amer. Math. Soc. 43 (1938) 258-270. | JFM 64.0714.03 | MR 1501942 | Zbl 0018.17403

[13] Minkowski H., Allgemeine Lehrsätze über die konvexen Polyeder, Nachr. Ges. Wiss. Göttingen (1897) 198-219. | JFM 28.0427.01

[14] Minkowski H., Volumen and Oberfläche, Math. Ann. 57 (1903) 447-495. | JFM 34.0649.01 | MR 1511220

[15] Miranda C., Su un problema di Minkowski, Rend. Sem. Mat. Roma 3 (1939) 96- 108. | JFM 65.0828.01 | MR 518 | Zbl 0021.35701

[16] Nirenberg L., The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953) 337-394. | MR 58265 | Zbl 0051.12402

[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 1085136 | Zbl 0746.53006