Geodesic
Curvature functionals for curves in the equi-affine plane
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 419-435 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail. Notice. An extended version of this article is available on arXiv:0912.4075.
DOI : 10.1007/s10587-011-0064-4
Classification : 49K05, 49K15, 49Q05, 53A15
Keywords: curvature functionals; variational problems; affine curves 
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Verpoort, Steven. Curvature functionals for curves in the equi-affine plane. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 419-435. doi: 10.1007/s10587-011-0064-4

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