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Unstable willmore surfaces of revolution subject to natural boundary conditions

Journal Article


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Abstract


  • In the class of surfaces with fixed boundary, critical points of the Willmore

    functional are naturally found to be those solutions of the Euler-Lagrange equation where

    the mean curvature on the boundary vanishes. We consider the case of symmetric surfaces

    of revolution in the setting where there are two families of stable solutions given by the

    catenoids. In this paper we demonstrate the existence of a third family of solutions which

    are unstable critical points of the Willmore functional, and which spatially lie between the

    upper and lower families of catenoids. Our method does not require any kind of smallness

    assumption, and allows us to derive some additional interesting qualitative properties of the

    solutions.

Authors


  •   Dall'Acqua, Anna (external author)
  •   Deckelnick, Klaus (external author)
  •   Wheeler, Glen E.

Publication Date


  • 2013

Geographic Focus


Citation


  • Dall'Acqua, A., Deckelnick, K. & Wheeler, G. (2013). Unstable willmore surfaces of revolution subject to natural boundary conditions. Calculus of Variations and Partial Differential Equations, 48 (3-4), 293-313.

Scopus Eid


  • 2-s2.0-84885622111

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3072&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2063

Has Global Citation Frequency


Number Of Pages


  • 20

Start Page


  • 293

End Page


  • 313

Volume


  • 48

Issue


  • 3-4

Place Of Publication


  • Germany

Abstract


  • In the class of surfaces with fixed boundary, critical points of the Willmore

    functional are naturally found to be those solutions of the Euler-Lagrange equation where

    the mean curvature on the boundary vanishes. We consider the case of symmetric surfaces

    of revolution in the setting where there are two families of stable solutions given by the

    catenoids. In this paper we demonstrate the existence of a third family of solutions which

    are unstable critical points of the Willmore functional, and which spatially lie between the

    upper and lower families of catenoids. Our method does not require any kind of smallness

    assumption, and allows us to derive some additional interesting qualitative properties of the

    solutions.

Authors


  •   Dall'Acqua, Anna (external author)
  •   Deckelnick, Klaus (external author)
  •   Wheeler, Glen E.

Publication Date


  • 2013

Geographic Focus


Citation


  • Dall'Acqua, A., Deckelnick, K. & Wheeler, G. (2013). Unstable willmore surfaces of revolution subject to natural boundary conditions. Calculus of Variations and Partial Differential Equations, 48 (3-4), 293-313.

Scopus Eid


  • 2-s2.0-84885622111

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3072&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2063

Has Global Citation Frequency


Number Of Pages


  • 20

Start Page


  • 293

End Page


  • 313

Volume


  • 48

Issue


  • 3-4

Place Of Publication


  • Germany