The Christoffel-Minkowski Problem II: Weingarten Curvature Equations*
Pengfei Guan , Changshou Lin , Xi'nan Ma
Chinese Annals of Mathematics, Series B ›› 2006, Vol. 27 ›› Issue (6) : 595 -614.
The Christoffel-Minkowski Problem II: Weingarten Curvature Equations*
In this paper the authors discuss the existence and convexity of hypersurfaces with prescribed Weingarten curvature.
Existence / Convexity / Weingarten curvature / 35J60 / 58G11
| [1] |
|
| [2] |
Alexandrov, A. D., Uniqueness theorems for surfaces in the large I, Vestnik Leningrad Univ., 11, 1956, 5–17 = Amer. Soc. Trans. Ser. 2, 21, 1962, 341–354. |
| [3] |
|
| [4] |
|
| [5] |
Caffarelli, L. A., Nirenberg, L. and Spruck, J., Nonlinear second order elliptic equations IV: Starshaped compactWeingarten hypersurfaces, Current Topics in Partial Differential Equations, Y. Ohya, K. Kasahara and N. Shimakura (eds.), Kinokunize, Tokyo, 1985, 1–26. |
| [6] |
|
| [7] |
|
| [8] |
Gerhardt, C., Closed Weingarten hypersurfaces in space forms, Geometric Analysis and the Calculus of Variation, F. Fort (ed.), International Press, Boston, 1996, 71–98. |
| [9] |
|
| [10] |
Guan, P. and Lin, C. S., On the equation det(u ij +δ ij u) = u p f(x) on S n, NCTS in Tsing-Hua University, 2000, preprint. |
| [11] |
|
| [12] |
|
| [13] |
|
| [14] |
|
| [15] |
|
| [16] |
|
| [17] |
Yau, S.-T., Problem section, Seminar on Differential Geometry, Ann. of Math. Stud., 102, Princeton Univ. Press, 1982, 669–706. |
| [18] |
|
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