Publikation: Appendix to: Convexity estimates for flows by powers of the mean curvature
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2006
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Schulze, Felix
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Annali della Scuola Normale Superiore di Pisa : Classe di Scienze. 2006, 5(5), pp. 273-277. ISSN 0036-9918
Zusammenfassung
We study the evolution of a closed, convex hypersurface in Rn+1 in direction of its normal vector, where the speed equals a power k≥1 of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to 1, depending only on k and n, then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere.
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SCHULZE, Felix, Oliver C. SCHNÜRER, 2006. Appendix to: Convexity estimates for flows by powers of the mean curvature. In: Annali della Scuola Normale Superiore di Pisa : Classe di Scienze. 2006, 5(5), pp. 273-277. ISSN 0036-9918BibTex
@article{Schulze2006Appen-41191,
year={2006},
title={Appendix to: Convexity estimates for flows by powers of the mean curvature},
url={http://www.numdam.org/item/ASNSP_2006_5_5_2_261_0},
number={5},
volume={5},
issn={0036-9918},
journal={Annali della Scuola Normale Superiore di Pisa : Classe di Scienze},
pages={273--277},
author={Schulze, Felix and Schnürer, Oliver C.}
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<dcterms:abstract xml:lang="eng">We study the evolution of a closed, convex hypersurface in Rn+1 in direction of its normal vector, where the speed equals a power k≥1 of the mean curvature. We show that if initially the ratio of the biggest and smallest principal curvatures at every point is close enough to 1, depending only on k and n, then this is maintained under the flow. As a consequence we obtain that, when rescaling appropriately as the flow contracts to a point, the evolving surfaces converge to the unit sphere.</dcterms:abstract>
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