145,653 research outputs found
Stability of the surface area preserving mean curvature flow in Euclidean space
We show that the surface area preserving mean curvature flow in Euclidean
space exists for all time and converges exponentially to a round sphere, if
initially the L^2-norm of the traceless second fundamental form is small (but
the initial hypersurface is not necessarily convex).Comment: 17 page
A Generalization of the Doubling Construction for Sums of Squares Identities
The doubling construction is a fast and important way to generate new
solutions to the Hurwitz problem on sums of squares identities from any known
ones. In this short note, we generalize the doubling construction and obtain
from any given admissible triple a series of new ones
for all positive integer , where is the
Hurwitz-Radon function
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