Journal of Differential Geometry
- J. Differential Geom.
- Volume 80, Number 3 (2008), 433-451.
Higher regularity of the inverse mean curvature flow
We prove higher regularity properties of inverse mean curvature flow in Euclidean space: A sharp lower bound for the mean curvature is derived for star-shaped surfaces, independently of the initial mean curvature. It is also shown that solutions to the inverse mean curvature flow are smooth if the mean curvature is bounded from below. As a consequence we show that weak solutions of the inverse mean curvature flow are smooth for large times, beginning from the first time where a surface in the evolution is star-shaped.
J. Differential Geom., Volume 80, Number 3 (2008), 433-451.
First available in Project Euclid: 7 November 2008
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Huisken , Gerhard; Ilmanen, Tom. Higher regularity of the inverse mean curvature flow. J. Differential Geom. 80 (2008), no. 3, 433--451. doi:10.4310/jdg/1226090483. https://projecteuclid.org/euclid.jdg/1226090483