Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

Heiko Kröner and Julian Scheuer

Mathematische Nachrichten, 2019, vol. 292, issue 7, 1514-1529

Abstract: We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form F−p, where p>1 and F is a positive, strictly monotone and 1‐homogeneous curvature function. In particular this class includes the mean curvature F=H. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews–McCoy–Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power p>1 loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1002/mana.201700370

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:mathna:v:292:y:2019:i:7:p:1514-1529

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0025-584X

Access Statistics for this article

Mathematische Nachrichten is currently edited by Robert Denk

More articles in Mathematische Nachrichten from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().