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Convexity estimates for flows by powers of the mean curvature
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Schulze, Felix (2006) Convexity estimates for flows by powers of the mean curvature. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, 5 (2). pp. 261-277.
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Official URL: http://www.numdam.org/item/ASNSP_2006_5_5_2_261_0
Abstract
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.
| Item Type: | Journal Article | ||||
|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||
| Journal or Publication Title: | Annali della Scuola Normale Superiore di Pisa - Classe di Scienze | ||||
| Publisher: | Scuola Normale Superiore, Pisa | ||||
| Official Date: | 2006 | ||||
| Dates: |
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| Volume: | 5 | ||||
| Number: | 2 | ||||
| Page Range: | pp. 261-277 | ||||
| Status: | Peer Reviewed | ||||
| Publication Status: | Published | ||||
| Access rights to Published version: | Restricted or Subscription Access |
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