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- W4313445050 abstract "A weak notion of elastic energy for (not necessarily regular) rectifiable curves in any space dimension is proposed. Our $p$-energy is defined through a relaxation process, where a suitable $p$-rotation of inscribed polygonals is adopted. The discrete $p$-rotation we choose has a geometric flavor: a polygonal is viewed as an approximation to a smooth curve and hence its discrete curvature is spread out into a smooth density. For any exponent $p$ greater than one, the $p$-energy is finite if and only if the arc-length parameterization of the curve has a second order summability with the same growth exponent. In that case, moreover, the energy agrees with the natural extension of the integral of the $p$-th power of the scalar curvature. Finally, a comparison with other definitions of discrete curvatures is discussed." @default.
- W4313445050 created "2023-01-06" @default.
- W4313445050 creator A5017963438 @default.
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- W4313445050 date "2022-12-29" @default.
- W4313445050 modified "2023-10-18" @default.
- W4313445050 title "Weak elastic energy of irregular curves" @default.
- W4313445050 doi "https://doi.org/10.48550/arxiv.2212.14380" @default.
- W4313445050 hasPublicationYear "2022" @default.
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