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Displaying similar documents to “Semicontinuity and relaxation properties of a curvature depending functional in 2D”

Base points of polar curves

Eduardo Casas-Alvero (1991)

Annales de l'institut Fourier

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The base points of the system of polar curves of an irreducible algebroid plane curve with general moduli are determined. As consequences a lower bound for the Tjurina number and many continuous analytic invariants of the curve are found.

Characterization of compact subsets of curves with ω-continuous derivatives

Marcin Pilipczuk (2011)

Fundamenta Mathematicae

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We give a characterization of compact subsets of finite unions of disjoint finite-length curves in ℝⁿ with ω-continuous derivative and without self-intersections. Intuitively, our condition can be formulated as follows: there exists a finite set of regular curves covering a compact set K iff every triple of points of K behaves like a triple of points of a regular curve. This work was inspired by theorems by Jones, Okikiolu, Schul and others that characterize compact...