146,955 research outputs found

    Stability of the surface area preserving mean curvature flow in Euclidean space

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    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

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    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 [r,s,n][r,s,n] a series of new ones [r+ρ(2m1),2ms,2mn][r+\rho(2^{m-1}),2^ms,2^mn] for all positive integer mm, where ρ\rho is the Hurwitz-Radon function
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