Appendix to: Convexity estimates for flows by powers of the mean curvature

Publikationstyp: Zeitschriftenartikel
Publikationsstatus: Published
Autor/innen: Schulze, Felix; Schnürer, Oliver C.
Erscheinungsjahr: 2006
Erschienen in: Annali della Scuola Normale Superiore di Pisa : Classe di Scienze ; 5 (2006), 5. - S. 273-277. - ISSN 0036-9918
URL der Originalveröffentlichung: http://www.numdam.org/item/ASNSP_2006_5_5_2_261_0, Letzter Zugriff am 12. Jan 2018
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.
Fachgebiet (DDC): 510 Mathematik

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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. 5(5), pp. 273-277. ISSN 0036-9918

@article{Schulze2006Appen-41191, 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}, year={2006}, 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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