Displaying similar documents to “Hölder regularity of two-dimensional almost-minimal sets in ℝ n ”

Hölder regularity of three-dimensional minimal cones in ℝⁿ

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.

C 1 -minimal subsets of the circle

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 C 1 -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.

Noninvertible minimal maps

Sergiĭ Kolyada, L'ubomír Snoha, Sergeĭ Trofimchuk (2001)

Fundamenta Mathematicae

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For a discrete dynamical system given by a compact Hausdorff space X and a continuous selfmap f of X the connection between minimality, invertibility and openness of f is investigated. It is shown that any minimal map is feebly open, i.e., sends open sets to sets with nonempty interiors (and if it is open then it is a homeomorphism). Further, it is shown that if f is minimal and A ⊆ X then both f(A) and f - 1 ( A ) share with A those topological properties which describe how large a set is. Using...

On lower Lipschitz continuity of minimal points

Ewa M. Bednarczuk (2000)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we investigate the lower Lipschitz continuity of minimal points of an arbitrary set A depending upon a parameter u . Our results are formulated with the help of the modulus of minimality. The crucial requirement which allows us to derive sufficient conditions for lower Lipschitz continuity of minimal points is that the modulus of minimality is at least linear. The obtained results can be directly applied to stability analysis of vector optimization problems.

Products of Snowflaked Euclidean Lines Are Not Minimal for Looking Down

Matthieu Joseph, Tapio Rajala (2017)

Analysis and Geometry in Metric Spaces

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We show that products of snowflaked Euclidean lines are not minimal for looking down. This question was raised in Fractured fractals and broken dreams, Problem 11.17, by David and Semmes. The proof uses arguments developed by Le Donne, Li and Rajala to prove that the Heisenberg group is not minimal for looking down. By a method of shortcuts, we define a new distance d such that the product of snowflaked Euclidean lines looks down on (RN , d), but not vice versa.

The local regularity of soap films after Jean Taylor

Guy David (2008)

Journées Équations aux dérivées partielles

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The following text is a minor modification of the transparencies that were used in the conference; please excuse the often telegraphic style. The main goal of the series of lectures is a presentation (with some proofs) of Jean Taylor’s celebrated theorem on the regularity of almost minimal sets of dimension 2 in ℝ 3 , and a few more recent extensions or perspectives. Some of the results presented below are work of, or with T. De Pauw, V. Feuvrier A. Lemenant, and T. Toro. ...