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A counterexample regarding a two-phase problem for harmonic measure in VMO

Tolsa X.
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The Jordan curve theorem and the Schönflies theorem in weak second-order arithmetic

Archive for Mathematical Logic, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Keita Yokoyama
exaly   +3 more sources

The Jordan Curve theorem

Resonance, 1999
exaly   +3 more sources

Tverberg’s proof of the Jordan closed curve theorem

St. Petersburg Mathematical Journal, 2016
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Paramonov, P. V., Fedorovsky, K. Yu.
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The traveling salesman theorem for Jordan curves

Advances in Mathematics, 2022
Peter Jones' traveling salesman theorem [\textit{P. W. Jones}, Invent. Math. 102, No. 1, 1--15 (1990; Zbl 0731.30018)], says that given a set \(E\subset \mathbb{R}^2\), \(E\) can be covered by a curve \(\Gamma\) with length \[ \ell(\Gamma) \simeq \mathrm{diam}(E) + \sum_Q \beta_E(Q)^2\mathrm{diam}(Q), \] where the sum is over dyadic cubes in \( \mathbb{
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Erdös-Turán theorems on a system of Jordan curves and arcs

Constructive Approximation, 1991
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Blatt, Hans-Peter, Grothmann, René
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What is the Jordan Curve Theorem?

The American Mathematical Monthly, 1942
(1942). What is the Jordan Curve Theorem? The American Mathematical Monthly: Vol. 49, No. 5, pp. 281-286.
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A Jordan Curve Theorem in the Digital Plane

2011
We study a certain Alexandroff topology on Z2 and some of its quotient topologies including the Khalimsky one. By proving an analogue of the Jordan curve theorem for this topology we show that it provides a large variety of digital Jordan curves. Some consequences of this result are discussed, too.
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The Jordan Curve Theorem for Piecewise Smooth Curves

The American Mathematical Monthly, 1969
(1969). The Jordan Curve Theorem for Piecewise Smooth Curves. The American Mathematical Monthly: Vol. 76, No. 6, pp. 605-610.
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