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Minkowski and packing Dimension comparisons for sets with Reifenberg\n properties

2011/01/18 by Amos N. Koeller, Koeller, Amos N.
Mathematics · Computer Science · #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.1101.3596

Abstract

In Koeller citekoerprops the twelve variants of the Reifenberg properties\nknown to be instrumental in the theory of minimal surfaces were classified with\nrespect to various Hausdorff measure based measure theoretic properties. The\nclassification lead to the consideration of fine geometric properties and a\nconnection to fractal geometry. The current work develops this connection and\nextends the classification to consider Minkowski-dimension, packing dimension,\nmeasure, and rectifiability, and the equality of packing and Hausdorff measures\nwith interesting results.\n

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