Isoperimetric inequalities for immersed closed spherical curves
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- by Joel L. Weiner PDF
- Proc. Amer. Math. Soc. 120 (1994), 501-506 Request permission
Abstract:
Let $\alpha :{S^1} \to {S^2}$ be a ${C^2}$ immersion with length $L$ and total curvature $K$. If $\alpha$ is regularly homotopic to a circle traversed once then ${L^2} + {K^2} \geqslant 4{\pi ^2}$ with equality if and only if $\alpha$ is a circle traversed once. If $\alpha$ has nonnegative geodesic curvature and multiple points then $L + K \geqslant 4\pi$ with equality if and only if $\alpha$ is a great circle traversed twice.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 501-506
- MSC: Primary 53A04; Secondary 53C42
- DOI: https://doi.org/10.1090/S0002-9939-1994-1163337-4
- MathSciNet review: 1163337