메뉴 건너뛰기




Volumn 17, Issue 6, 2000, Pages 733-751

A logarithmic Gauss curvature flow and the Minkowski problem

Author keywords

Asymptotic behavior; Gauss curvature; Minkowski problem; Parabolic Monge Amp re equation

Indexed keywords


EID: 0013120659     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0294-1449(00)00053-6     Document Type: Article
Times cited : (106)

References (18)
  • 1
    • 0030092746 scopus 로고    scopus 로고
    • Contraction of convex hypersurfaces by their affine normal
    • Andrews B., Contraction of convex hypersurfaces by their affine normal, J. Differential Geom. 43 (1996) 207-229.
    • (1996) J. Differential Geom. , vol.43 , pp. 207-229
    • Andrews, B.1
  • 2
    • 0000342399 scopus 로고    scopus 로고
    • Evolving convex curves
    • Andrews B., Evolving convex curves, Calc. Var. PDE 1 (1998) 315-371.
    • (1998) Calc. Var. PDE , vol.1 , pp. 315-371
    • Andrews, B.1
  • 3
    • 84980163110 scopus 로고
    • On the regularity of the solution of the n-dimensional Minkowski problem
    • 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.
    • (1976) Comm. Pure Appl. Math. , vol.29 , pp. 495-516
    • Cheng, S.Y.1    Yau, S.T.2
  • 4
    • 84990622731 scopus 로고
    • Deforming a hypersurface by its Gauss-Kronecker curvature
    • Chou K. (Tso, K.), Deforming a hypersurface by its Gauss-Kronecker curvature, Comm. Pure Appl. Math 38 (1985) 867-882.
    • (1985) Comm. Pure Appl. Math , vol.38 , pp. 867-882
    • Chou, K.1
  • 5
    • 84972541648 scopus 로고
    • Convex hypersurfaces with prescribed Gauss-Kronecker curvature
    • Chou K. (Tso, K.), Convex hypersurfaces with prescribed Gauss-Kronecker curvature, J. Differential Geom. 34 (1991) 389-410.
    • (1991) J. Differential Geom. , vol.34 , pp. 389-410
    • Chou, K.1
  • 6
    • 0040531581 scopus 로고    scopus 로고
    • Anisotropic curvature flows for plane curves
    • Chou K., Zhu X., Anisotropic curvature flows for plane curves, Duke Math. J. 97 (1999) 579-619.
    • (1999) Duke Math. J. , vol.97 , pp. 579-619
    • Chou, K.1    Zhu, X.2
  • 7
    • 84972529405 scopus 로고
    • Deforming convex hypersurfaces by the n-th root of the Gaussian curvature
    • Chow B., Deforming convex hypersurfaces by the n-th root of the Gaussian curvature, J. Differential Geom. 22 (1985) 117-138.
    • (1985) J. Differential Geom. , vol.22 , pp. 117-138
    • Chow, B.1
  • 8
    • 84966244873 scopus 로고
    • Shapes of worn stones
    • Firey W., Shapes of worn stones, Mathematica 21 (1974) 1-11.
    • (1974) Mathematica , vol.21 , pp. 1-11
    • Firey, W.1
  • 9
    • 0345788532 scopus 로고
    • Evolving plane curves by curvature in relative geometries II
    • Gage M.E., Li Y., Evolving plane curves by curvature in relative geometries II, Duke Math. J. 75 (1994) 79-98.
    • (1994) Duke Math. J. , vol.75 , pp. 79-98
    • Gage, M.E.1    Li, Y.2
  • 10
    • 84972495800 scopus 로고
    • Flow of non convex hypersurfaces into spheres
    • Gerhardt C., Flow of non convex hypersurfaces into spheres, J. Differential Geom. 32 (1990) 299-314.
    • (1990) J. Differential Geom. , vol.32 , pp. 299-314
    • Gerhardt, C.1
  • 12
    • 0001480062 scopus 로고
    • On differential geometry in the large, I (Minkowski's problem)
    • Lewy H., On differential geometry in the large, I (Minkowski's problem), Trans. Amer. Math. Soc. 43 (1938) 258-270.
    • (1938) Trans. Amer. Math. Soc. , vol.43 , pp. 258-270
    • Lewy, H.1
  • 13
    • 0002534146 scopus 로고
    • Allgemeine Lehrsätze über die konvexen Polyeder
    • Minkowski H., Allgemeine Lehrsätze über die konvexen Polyeder, Nachr. Ges. Wiss. Göttingen (1897) 198-219.
    • (1897) Nachr. Ges. Wiss. Göttingen , pp. 198-219
    • Minkowski, H.1
  • 14
    • 33748504072 scopus 로고
    • Volumen and Oberfläche
    • Minkowski H., Volumen and Oberfläche, Math. Ann. 57 (1903) 447-495.
    • (1903) Math. Ann. , vol.57 , pp. 447-495
    • Minkowski, H.1
  • 15
    • 0346621865 scopus 로고
    • Su un problema di Minkowski
    • Miranda C., Su un problema di Minkowski, Rend. Sem. Mat. Roma 3 (1939) 96-108.
    • (1939) Rend. Sem. Mat. Roma , vol.3 , pp. 96-108
    • Miranda, C.1
  • 16
    • 84980088567 scopus 로고
    • The Weyl and Minkowski problems in differential geometry in the large
    • Nirenberg L., The Weyl and Minkowski problems in differential geometry in the large, Comm. Pure Appl. Math. 6 (1953) 337-394.
    • (1953) Comm. Pure Appl. Math. , vol.6 , pp. 337-394
    • Nirenberg, L.1
  • 18
    • 84972517049 scopus 로고
    • On the expansion of convex hypersurfaces by symmetric functions of their principal radii of curvature
    • 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.
    • (1991) J. Differential Geom. , vol.33 , pp. 91-125
    • Urbas, J.I.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.