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- W2144405726 abstract "We deflne the total curvature of a semialgebraic graph i ‰ R 3 as an integral K(i) = R i d, where is a certain Borel measure completely determined by the local extrinsic geometry of i. We prove that it satisfles the Chern-Lashof inequality K(i) ‚ b(i), where b(i) = b0(i) +b1(i), and we completely characterize those graphs for which we have equality. We also prove the following unknottedness result: if i ‰ R 3 is homeomorphic to the suspension of an n-point set, and satisfles the inequality K(i) 0 there exists a knotted semialgebraic embedding i of G in R 3 satisfying K(i) < + b(i)." @default.
- W2144405726 created "2016-06-24" @default.
- W2144405726 creator A5063741270 @default.
- W2144405726 date "2008-06-23" @default.
- W2144405726 modified "2023-09-27" @default.
- W2144405726 title "ON THE TOTAL CURVATURE OF SEMIALGEBRAIC GRAPHS" @default.
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