메뉴 건너뛰기




Volumn 78, Issue 7, 1999, Pages 667-700

General curvature estimates for stable H-surfaces immersed into a space form

Author keywords

Constant mean curvature; Curvature estimates; Morse index; Stability

Indexed keywords


EID: 0033197235     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(99)00025-2     Document Type: Article
Times cited : (10)

References (22)
  • 2
    • 0001271263 scopus 로고
    • Surfaces of mean curvature one in hyperbolic space
    • R. Bryant, Surfaces of mean curvature one in hyperbolic space, Astérisque 154-155 (1987) 321-347.
    • (1987) Astérisque , vol.154-155 , pp. 321-347
    • Bryant, R.1
  • 3
    • 0000839683 scopus 로고
    • Simons' equation revisited
    • P. Bérard, Simons' equation revisited, An. Acad. Bras. Ci. 66 (1994) 397-403.
    • (1994) An. Acad. Bras. Ci. , vol.66 , pp. 397-403
    • Bérard, P.1
  • 4
    • 0031280557 scopus 로고    scopus 로고
    • Sur l'opérateur de stabilité des sous-variétés à courbure moyenne constante dans l'espace hyperbolique
    • P. Castillon, Sur l'opérateur de stabilité des sous-variétés à courbure moyenne constante dans l'espace hyperbolique, Manuscr. Math. 94 (1997) 385-400.
    • (1997) Manuscr. Math. , vol.94 , pp. 385-400
    • Castillon, P.1
  • 5
    • 85030065630 scopus 로고
    • Geometric properties of stable noncompact constant mean curvature surfaces
    • Dissertation, Rheinische Friedrich-Wilhems-Universität Bonn. Universität Bonn, Math. Institut, Bonn (1991) iv+65 pp
    • L.-F. Cheung, Geometric properties of stable noncompact constant mean curvature surfaces, Dissertation, Rheinische Friedrich-Wilhems-Universität Bonn, 1990. Bonner Math. Schriften, 220. Universität Bonn, Math. Institut, Bonn (1991) iv+65 pp.
    • (1990) Bonner Math. Schriften , vol.220
    • Cheung, L.-F.1
  • 6
    • 0000071944 scopus 로고
    • Interior curvature estimates for hypersurfaces of prescrided mean curvature
    • K. Ecker and G. Huisken, Interior curvature estimates for hypersurfaces of prescrided mean curvature, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 6 (1989) 251-260.
    • (1989) Ann. Inst. Henri Poincaré, Anal. Non Linéaire , vol.6 , pp. 251-260
    • Ecker, K.1    Huisken, G.2
  • 7
    • 0000362154 scopus 로고
    • On complete minimal surfaces with finite Morse index in three manifolds
    • D. Fischer-Colbrie, On complete minimal surfaces with finite Morse index in three manifolds, Inventiones Math. 82 (1987) 121-132.
    • (1987) Inventiones Math. , vol.82 , pp. 121-132
    • Fischer-Colbrie, D.1
  • 8
    • 84980187204 scopus 로고
    • The structure of complete minimal surfaces in 3-manifolds of non-negative scalar curvature
    • D. Fischer-Colbrie and R. Schoen, The structure of complete minimal surfaces in 3-manifolds of non-negative scalar curvature, Comm. Pure Appl. Math. 33 (1980) 199-211.
    • (1980) Comm. Pure Appl. Math. , vol.33 , pp. 199-211
    • Fischer-Colbrie, D.1    Schoen, R.2
  • 9
    • 85030074836 scopus 로고    scopus 로고
    • Thesis in progress, IMPA
    • R. Freire de Lima, Thesis in progress, IMPA, 1998.
    • (1998)
    • De Lima, R.F.1
  • 11
    • 84980186088 scopus 로고
    • Sobolev and isoperimetric inequalities for Riemannian submanifolds
    • D. Hoffman and J. Struck, Sobolev and isoperimetric inequalities for Riemannian submanifolds, Comm. Pure Appl. Math. 27 (1974) 715-727.
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 715-727
    • Hoffman, D.1    Struck, J.2
  • 13
    • 0009317060 scopus 로고
    • An extension of certain results in function theory to a class of surfaces
    • R. Osserman, An extension of certain results in function theory to a class of surfaces, Proc. Nat. Acad. Sci. 45 (1959) 1031-1035.
    • (1959) Proc. Nat. Acad. Sci. , vol.45 , pp. 1031-1035
    • Osserman, R.1
  • 14
    • 85030060956 scopus 로고    scopus 로고
    • Private communication
    • H. Rosenberg, Private communication, 1998.
    • (1998)
    • Rosenberg, H.1
  • 15
    • 51249178867 scopus 로고
    • A priori estimates of the principal curvatures for immersions of prescribed mean curvature and a theorem of Bernstein type
    • F. Sauvigny, A priori estimates of the principal curvatures for immersions of prescribed mean curvature and a theorem of Bernstein type, Math. Z. 205 (1990) 567-582.
    • (1990) Math. Z. , vol.205 , pp. 567-582
    • Sauvigny, F.1
  • 16
    • 0001731162 scopus 로고
    • Estimates for stable minimal surfaces in three dimensional manifolds
    • E. Bombieri (Ed.), Annals of Math. Studies, Princeton University Press
    • R. Schoen, Estimates for stable minimal surfaces in three dimensional manifolds, in: E. Bombieri (Ed.), Seminar on Minimal Submanifolds, Annals of Math. Studies, Princeton University Press, 1983.
    • (1983) Seminar on Minimal Submanifolds
    • Schoen, R.1
  • 18
    • 0001114041 scopus 로고
    • Curvature estimates for minimal hypersurfaces
    • R. Schoen, L. Simon and S.-T. Yau, Curvature estimates for minimal hypersurfaces, Acta Math. 134 (1975) 275-288.
    • (1975) Acta Math. , vol.134 , pp. 275-288
    • Schoen, R.1    Simon, L.2    Yau, S.-T.3
  • 19
    • 0000969838 scopus 로고
    • Stability of complete noncompact surfaces with constant mean curvature
    • A. da Silveira, Stability of complete noncompact surfaces with constant mean curvature, Math. Ann. 277 (1987) 629-638.
    • (1987) Math. Ann. , vol.277 , pp. 629-638
    • Da Silveira, A.1
  • 20
    • 0002460686 scopus 로고
    • Minimal varieties in Riemannian manifolds
    • J. Simons, Minimal varieties in Riemannian manifolds, Annals of Math. 88 (1968) 62-105.
    • (1968) Annals of Math. , vol.88 , pp. 62-105
    • Simons, J.1
  • 21
    • 84980166805 scopus 로고
    • Gauss curvature estimates for surfaces of constant mean curvature
    • J. Spruck, Gauss curvature estimates for surfaces of constant mean curvature, Comm. Pure Appl. Math. 27 (1974) 547-557.
    • (1974) Comm. Pure Appl. Math. , vol.27 , pp. 547-557
    • Spruck, J.1
  • 22
    • 0009428253 scopus 로고
    • On stable surfaces of constant Gauss curvature in spaces forms
    • M. Traizet, On stable surfaces of constant Gauss curvature in spaces forms, Annals Global Anal. Geom. 13 (1995) 141-148.
    • (1995) Annals Global Anal. Geom. , vol.13 , pp. 141-148
    • Traizet, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.