Real Algebraic and Analytic Geometry Preprint Server

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Submission: 2003, March 27.

Abstract:
Let $M\subset \R^n$ be a smooth compact component of an algebraic hypersurface of degree $d$. Assume that $m$ is contained in a ball of radius $r$, we prove that the geodesic diameter of $M$ is bounded by $2r\nu(n)d(4d-5)^{n-2}$.

Mathematics Subject Classification (2000): 32Bxx, 34Cxx, 32Sxx, 14P10.

Keywords and Phrases: gradient trajectories, polynomials.

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