Minimal closed sets and maximal closed sets.
Nakaoka, Fumie, Oda, Nobuyuki (2006)
International Journal of Mathematics and Mathematical Sciences
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Nakaoka, Fumie, Oda, Nobuyuki (2006)
International Journal of Mathematics and Mathematical Sciences
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Asit Baran-Raha (1972)
Colloquium Mathematicae
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Jan Bochenek (1985)
Annales Polonici Mathematici
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Guido De Philippis, Emanuele Paolini (2009)
Rendiconti del Seminario Matematico della Università di Padova
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H. Fredricksen, E. J. Ionascu, F. Luca, P. Stănică (2008)
Acta Arithmetica
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L Moser (1959)
Acta Arithmetica
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Tien Duc Luu (2014)
Annales Polonici Mathematici
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We show the local Hölder regularity of Almgren minimal cones of dimension 3 in ℝⁿ away from their centers. The proof is almost elementary but we use the generalized theorem of Reifenberg. In the proof, we give a classification of points away from the center of a minimal cone of dimension 3 in ℝⁿ, into types ℙ, 𝕐 and 𝕋. We then treat each case separately and give a local Hölder parameterization of the cone.
J. Marshall Ash, A. Eduardo Gatto, Stephen Vági (1990)
Colloquium Mathematicae
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Aikawa, Hiroaki (1993)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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Pierre Michel (1975)
Publications mathématiques et informatique de Rennes
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Weber, Matthias J., Schröcker, Hans-Peter (2010)
Beiträge zur Algebra und Geometrie
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Jürg Schmid, Jürgen Schmidt (1987)
Colloquium Mathematicae
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Tomasz Downarowicz (2011)
Colloquium Mathematicae
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We construct an example of two commuting homeomorphisms S, T of a compact metric space X such that the union of all minimal sets for S is disjoint from the union of all minimal sets for T. In other words, there are no common minimal points. This answers negatively a question posed in [C-L]. We remark that Furstenberg proved the existence of "doubly recurrent" points (see [F]). Not only are these points recurrent under both S and T, but they recur along the same sequence of powers. Our...
Charles A. Stuart (1978)
Mathematische Zeitschrift
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Dusa McDuff (1981)
Annales de l'institut Fourier
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Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.