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Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions

Journal Article


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Abstract


  • Inspired by earlier results on the quasilinear mean curvature flow, and recent investigations

    of fully nonlinear curvature flow of closed hypersurfaces which are not convex, we

    consider contraction of axially symmetric hypersurfaces by convex, degree-one homogeneous

    fully nonlinear functions of curvature. With a natural class of Neumann boundary

    conditions, we show that evolving hypersurfaces exist for a finite maximal time. The maximal

    time is characterised by a curvature singularity at either boundary. Some results continue

    to hold in the cases of mixed Neumann–Dirichlet boundary conditions and more general

    curvature-dependent speeds.

Publication Date


  • 2014

Citation


  • McCoy, J. A., Mofarreh, F. Y. Y. & Williams, G. H. (2014). Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions. Annali di Matematica Pura ed Applicata, 193 (5), 1443-1455.

Scopus Eid


  • 2-s2.0-84929441310

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3274&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2265

Has Global Citation Frequency


Number Of Pages


  • 12

Start Page


  • 1443

End Page


  • 1455

Volume


  • 193

Issue


  • 5

Place Of Publication


  • Germany

Abstract


  • Inspired by earlier results on the quasilinear mean curvature flow, and recent investigations

    of fully nonlinear curvature flow of closed hypersurfaces which are not convex, we

    consider contraction of axially symmetric hypersurfaces by convex, degree-one homogeneous

    fully nonlinear functions of curvature. With a natural class of Neumann boundary

    conditions, we show that evolving hypersurfaces exist for a finite maximal time. The maximal

    time is characterised by a curvature singularity at either boundary. Some results continue

    to hold in the cases of mixed Neumann–Dirichlet boundary conditions and more general

    curvature-dependent speeds.

Publication Date


  • 2014

Citation


  • McCoy, J. A., Mofarreh, F. Y. Y. & Williams, G. H. (2014). Fully nonlinear curvature flow of axially symmetric hypersurfaces with boundary conditions. Annali di Matematica Pura ed Applicata, 193 (5), 1443-1455.

Scopus Eid


  • 2-s2.0-84929441310

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=3274&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/2265

Has Global Citation Frequency


Number Of Pages


  • 12

Start Page


  • 1443

End Page


  • 1455

Volume


  • 193

Issue


  • 5

Place Of Publication


  • Germany