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Volumn 161, Issue , 2012, Pages 19-29

The asymptotic shape of a boundary layer of symmetric willmore surfaces of revolution

Author keywords

Asymptotic shape; Boundary layer; Dirichlet boundary conditions; Willmore surfaces of revolution

Indexed keywords


EID: 84885579216     PISSN: 03733149     EISSN: 22966072     Source Type: Book Series    
DOI: 10.1007/978-3-0348-0249-9_2     Document Type: Chapter
Times cited : (8)

References (19)
  • 1
    • 0038374781 scopus 로고    scopus 로고
    • Existence of minimizing Willmore surfaces of prescribed genus
    • Bauer, M., Kuwert, E.: Existence of minimizing Willmore surfaces of prescribed genus. Int. Math. Res. Not. 2003(10), 553–576 (2003)
    • (2003) Int. Math. Res. Not , vol.2003 , Issue.10 , pp. 553-576
    • Bauer, M.1    Kuwert, E.2
  • 2
    • 0001874919 scopus 로고
    • A duality theorem for Willmore surfaces
    • Bryant, R.: A duality theorem for Willmore surfaces. J. Differ. Geom. 20, 23–53 (1984)
    • (1984) J. Differ. Geom , vol.20 , pp. 23-53
    • Bryant, R.1
  • 4
    • 2342475802 scopus 로고    scopus 로고
    • A finite element method for surface restoration with smooth boundary conditions
    • Clarenz, U., Diewald, U., Dziuk, G., Rumpf, M., Rusu, R.: A finite element method for surface restoration with smooth boundary conditions. Comput. Aided Geom. Des. 21, 427–445 (2004)
    • (2004) Comput. Aided Geom. Des , vol.21 , pp. 427-445
    • Clarenz, U.1    Diewald, U.2    Dziuk, G.3    Rumpf, M.4    Rusu, R.5
  • 5
    • 71149088551 scopus 로고    scopus 로고
    • Classical solutions to the Dirichlet problem for Willmore surfaces of revolution
    • Dall’Acqua, A., Deckelnick, K., Grunau, H.-Ch.: Classical solutions to the Dirichlet problem for Willmore surfaces of revolution. Adv. Calc. Var. 1, 379–397 (2008)
    • (2008) Adv. Calc. Var , vol.1 , pp. 379-397
    • Dall’Acqua, A.1    Deckelnick, K.2    Grunau, H.-Ch.3
  • 6
    • 79960350031 scopus 로고    scopus 로고
    • Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data
    • Dall’Acqua, A., Fröhlich, S., Grunau, H.-Ch., Schieweck, F.: Symmetric Willmore surfaces of revolution satisfying arbitrary Dirichlet boundary data. Adv. Calc. Var. 4, 1–81 (2011)
    • (2011) Adv. Calc. Var , vol.4 , pp. 1-81
    • Dall’Acqua, A.1    Fröhlich, S.2    Grunau, H.-Ch.3    Schieweck, F.4
  • 8
    • 84943997802 scopus 로고
    • Elastic properties of lipid bilayers: Theory and possible experiments
    • Helfrich, W.: Elastic properties of lipid bilayers: Theory and possible experiments. Z. Natur-forsch. C 28, 693–703 (1973)
    • (1973) Z. Natur-forsch. C , vol.28 , pp. 693-703
    • Helfrich, W.1
  • 9
    • 0013515695 scopus 로고
    • Ein Beweis der Willmoreschen Vermutung für Kanaltori
    • Hertrich-Jeromin, U., Pinkall, U.: Ein Beweis der Willmoreschen Vermutung für Kanaltori. J. Reine Angew. Math. 430, 21–34 (1992)
    • (1992) J. Reine Angew. Math , vol.430 , pp. 21-34
    • Hertrich-Jeromin, U.1    Pinkall, U.2
  • 11
    • 84972507666 scopus 로고
    • The total squared curvature of closed curves
    • Langer, J., Singer, D.: The total squared curvature of closed curves. J. Differ. Geom. 20, 1–22 (1984)
    • (1984) J. Differ. Geom , vol.20 , pp. 1-22
    • Langer, J.1    Singer, D.2
  • 12
    • 0000699786 scopus 로고
    • Curves in the hyperbolic plane and mean curvature of tori in 3-space
    • Langer, J., Singer, D.: Curves in the hyperbolic plane and mean curvature of tori in 3-space. Bull. Lond. Math. Soc. 16, 531–534 (1984)
    • (1984) Bull. Lond. Math. Soc , vol.16 , pp. 531-534
    • Langer, J.1    Singer, D.2
  • 13
    • 0001851007 scopus 로고
    • Boundary value problems for variational integrals involving surface curvatures
    • Nitsche, J.C.C.: Boundary value problems for variational integrals involving surface curvatures. Q. Appl. Math. 51, 363–387 (1993)
    • (1993) Q. Appl. Math , vol.51 , pp. 363-387
    • Nitsche, J.C.C.1
  • 14
    • 0035422313 scopus 로고    scopus 로고
    • Elastic theory of biomembranes
    • Ou-Yang, Z.: Elastic theory of biomembranes. Thin Solid Films 393, 19–23 (2001)
    • (2001) Thin Solid Films , vol.393 , pp. 19-23
    • Ou-Yang, Z.1
  • 17
    • 0000526405 scopus 로고
    • Existence of surfaces minimizing the Willmore functional
    • Simon, L.: Existence of surfaces minimizing the Willmore functional. Commun. Anal. Geom. 1, 281–326 (1993)
    • (1993) Commun. Anal. Geom , vol.1 , pp. 281-326
    • Simon, L.1
  • 18
    • 0002404150 scopus 로고
    • Über konforme Geometrie I: Grundlagen der konformen Flächentheorie
    • Thomsen, G.: Über konforme Geometrie I: Grundlagen der konformen Flächentheorie. Abh. Math. Semin. Univ. Hamb. 3, 31–56 (1923)
    • (1923) Abh. Math. Semin. Univ. Hamb , vol.3 , pp. 31-56
    • Thomsen, G.1
  • 19
    • 0004265477 scopus 로고
    • Oxford Science Publications, The Clarendon Press, Oxford University Press, New York
    • Willmore, T.J.: Riemannian Geometry. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York (1993)
    • (1993) Riemannian Geometry
    • Willmore, T.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.