Abstract
I began in [CZ] the study of the geometric meaning of discontinuities of approximating Hausdorff measures (cf. [F], §2. 10.1). Later those methods were developed and applied to questions regarding sets of constant width ([SZ], [St 1], [St 2]). In this paper I study some aspects regarding a plane rectifiable curve; precisely theor. 1.4 gives a sufficient continuity condition, while in §2 I pick out, on the rectifiable curve, subsets of the boundary of a set of constant width, which are responsible of the possible discontinuity. Symbols are explained at the beginning of each paragraph.
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Dedicated to Ennio De Giorgi on his sixtieth birthday
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© 1989 Birkhauser Boston
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Chiffi, A. (1989). Approximating Measures and Rectifiable Curves. In: Colombini, F., Marino, A., Modica, L., Spagnolo, S. (eds) Partial Differential Equations and the Calculus of Variations. Progress in Nonlinear Differential Equations and Their Applications, vol 1. Birkhäuser Boston. https://doi.org/10.1007/978-1-4615-9828-2_13
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DOI: https://doi.org/10.1007/978-1-4615-9828-2_13
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