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More mixed volume preserving curvature flows

Journal Article


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Abstract


  • We extend the results of McCoy (Calc Var Partial Differ Equ 24:131–154, 2005) to include several new cases where convex surfaces evolve to spheres under mixed volume preserving curvature flows, using recent results for unconstrained curvature flows and new regularity arguments in the constrained flow setting. We include results for speeds that are degree 1 homogeneous in the principal curvatures and indicate how, with sufficient curvature pinching conditions on the initial hypersurfaces, some results may be extended to speed homogeneous of degree α>1. In particular, these extensions require lower speed bounds that are obtained here without using estimates for equations of porous medium type, in contrast to most previous work.

Publication Date


  • 2017

Citation


  • McCoy, J. A. (2017). More mixed volume preserving curvature flows. Journal of Geometric Analysis, Online First 1-26.

Scopus Eid


  • 2-s2.0-85014208847

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7587&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6557

Number Of Pages


  • 25

Start Page


  • 1

End Page


  • 26

Volume


  • Online First

Abstract


  • We extend the results of McCoy (Calc Var Partial Differ Equ 24:131–154, 2005) to include several new cases where convex surfaces evolve to spheres under mixed volume preserving curvature flows, using recent results for unconstrained curvature flows and new regularity arguments in the constrained flow setting. We include results for speeds that are degree 1 homogeneous in the principal curvatures and indicate how, with sufficient curvature pinching conditions on the initial hypersurfaces, some results may be extended to speed homogeneous of degree α>1. In particular, these extensions require lower speed bounds that are obtained here without using estimates for equations of porous medium type, in contrast to most previous work.

Publication Date


  • 2017

Citation


  • McCoy, J. A. (2017). More mixed volume preserving curvature flows. Journal of Geometric Analysis, Online First 1-26.

Scopus Eid


  • 2-s2.0-85014208847

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7587&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6557

Number Of Pages


  • 25

Start Page


  • 1

End Page


  • 26

Volume


  • Online First