A logarithmic Gauss curvature flow and the Minkowski problem

Kai-Seng Chou; Xu-Jia Wang

Annales de l'I.H.P. Analyse non linéaire (2000)

  • Volume: 17, Issue: 6, page 733-751
  • ISSN: 0294-1449

How to cite

top

Chou, Kai-Seng, and Wang, Xu-Jia. "A logarithmic Gauss curvature flow and the Minkowski problem." Annales de l'I.H.P. Analyse non linéaire 17.6 (2000): 733-751. <http://eudml.org/doc/78507>.

@article{Chou2000,
author = {Chou, Kai-Seng, Wang, Xu-Jia},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {parabolic Monge-Ampr̀e equation; Gauss curvature; Minkowski problem; Asymptotic behavior},
language = {eng},
number = {6},
pages = {733-751},
publisher = {Gauthier-Villars},
title = {A logarithmic Gauss curvature flow and the Minkowski problem},
url = {http://eudml.org/doc/78507},
volume = {17},
year = {2000},
}

TY - JOUR
AU - Chou, Kai-Seng
AU - Wang, Xu-Jia
TI - A logarithmic Gauss curvature flow and the Minkowski problem
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2000
PB - Gauthier-Villars
VL - 17
IS - 6
SP - 733
EP - 751
LA - eng
KW - parabolic Monge-Ampr̀e equation; Gauss curvature; Minkowski problem; Asymptotic behavior
UR - http://eudml.org/doc/78507
ER -

References

top
  1. [1] Andrews B., Contraction of convex hypersurfaces by their affine normal, J. Differential Geom.43 (1996) 207-229. Zbl0858.53005MR1424425
  2. [2] Andrews B., Evolving convex curves, Calc. Var. PDE1 (1998) 315-371. Zbl0931.53030MR1660843
  3. [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. Zbl0363.53030MR423267
  4. [4] Chou K. ( Tso, K.), Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure Appl. Math38 (1985) 867-882. Zbl0612.53005MR812353
  5. [5] Chou K. ( Tso, K.), Convex hypersurfaces with prescribed Gauss-Kronecker curvature, J. Differential Geom.34 (1991) 389-410. Zbl0723.53041MR1131436
  6. [6] Chou K., Zhu X., Anisotropic curvature flows for plane curves, Duke Math. J.97 (1999) 579-619. Zbl0946.53033MR1682990
  7. [7] Chow B., Deforming convex hypersurfaces by the n-th root of the Gaussian curvature, J. Differential Geom.22 (1985) 117-138. Zbl0589.53005MR826427
  8. [8] Firey W., Shapes of worn stones, Mathematica21 (1974) 1-11. Zbl0311.52003MR362045
  9. [9] Gage M.E., Li Y., Evolving plane curves by curvature in relative geometries II, Duke Math. J.75 (1994) 79-98. Zbl0811.53033MR1284816
  10. [10] Gerhardt C., Flow of non convex hypersurfaces into spheres, J. Differential Geom.32 (1990) 299-314. Zbl0708.53045
  11. [11] Krylov N.V., Nonlinear Elliptic and Parabolic Equations of the Second Order, D. Reidel, 1987. Zbl0619.35004MR901759
  12. [12] Lewy H., On differential geometry in the large, I (Minkowski's problem), Trans. Amer. Math. Soc.43 (1938) 258-270. Zbl0018.17403MR1501942
  13. [13] Minkowski H., Allgemeine Lehrsätze über die konvexen Polyeder, Nachr. Ges. Wiss. Göttingen (1897) 198-219. Zbl28.0427.01JFM28.0427.01
  14. [14] Minkowski H., Volumen and Oberfläche, Math. Ann.57 (1903) 447-495. MR1511220JFM34.0649.01
  15. [15] Miranda C., Su un problema di Minkowski, Rend. Sem. Mat. Roma3 (1939) 96- 108. Zbl0021.35701MR518
  16. [16] Nirenberg L., The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math.6 (1953) 337-394. Zbl0051.12402MR58265
  17. [17] Pogorelov A.V., The Multidimensional Minkowski Problem, J. Wiley, New York, 1978. Zbl0387.53023
  18. [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. Zbl0746.53006MR1085136

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.