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The mean curvature and volume growth of complete noncompact submanifolds

โœ Scribed by Leung-Fu Cheung; Pui-Fai Leung


Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
356 KB
Volume
8
Category
Article
ISSN
0926-2245

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โœฆ Synopsis


We show that a complete noncompact submanifold with bounded mean curvature in the Euclidean or hyperbolic space has at least linear volume growth. We apply this to obtain some results on submanifolds of parallel mean curvature.


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โœ M. Brassel; E. Bretin ๐Ÿ“‚ Article ๐Ÿ“… 2011 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 529 KB

This paper is concerned with the motion of a time-dependent hypersurface \* (t) in R d that evolves with a normal velocity where j is the mean curvature of \*X(t), and g is an external forcing term. Phase field approximation of this motion leads to the Allen-Cahn equation where is an approximation