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Convexity estimates for surfaces moving by curvature functions

Journal Article


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Abstract


  • We consider the evolution of compact surfaces by fully nonlinear, parabolic curvature

    ows for which the normal speed is given by a smooth, degree one homogeneous function of the principal curvatures of the evolving surface. Under no further restrictions on the speed function, we prove that initial surfaces on which the speed is positive become weakly convex at a singularity of the flow. This generalises the corresponding result [26] of Huisken

    and Sinestrari for the mean curvature ow to the largest possible class of degree one homogeneous surface flows.

Authors


  •   Andrews, Ben H. (external author)
  •   Langford, Mat (external author)
  •   McCoy, James A.

Publication Date


  • 2015

Citation


  • Andrews, B., Langford, M. & McCoy, J. (2015). Convexity estimates for surfaces moving by curvature functions. Journal of Differential Geometry, 99 (1), 47-75.

Scopus Eid


  • 2-s2.0-84918773570

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4460&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3443

Has Global Citation Frequency


Number Of Pages


  • 28

Start Page


  • 47

End Page


  • 75

Volume


  • 99

Issue


  • 1

Place Of Publication


  • United States

Abstract


  • We consider the evolution of compact surfaces by fully nonlinear, parabolic curvature

    ows for which the normal speed is given by a smooth, degree one homogeneous function of the principal curvatures of the evolving surface. Under no further restrictions on the speed function, we prove that initial surfaces on which the speed is positive become weakly convex at a singularity of the flow. This generalises the corresponding result [26] of Huisken

    and Sinestrari for the mean curvature ow to the largest possible class of degree one homogeneous surface flows.

Authors


  •   Andrews, Ben H. (external author)
  •   Langford, Mat (external author)
  •   McCoy, James A.

Publication Date


  • 2015

Citation


  • Andrews, B., Langford, M. & McCoy, J. (2015). Convexity estimates for surfaces moving by curvature functions. Journal of Differential Geometry, 99 (1), 47-75.

Scopus Eid


  • 2-s2.0-84918773570

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4460&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3443

Has Global Citation Frequency


Number Of Pages


  • 28

Start Page


  • 47

End Page


  • 75

Volume


  • 99

Issue


  • 1

Place Of Publication


  • United States