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  Pointwise differentiability of higher order for sets

Menne, U. (2019). Pointwise differentiability of higher order for sets. Annals of Global Analysis and Geometry. doi:10.1007/s10455-018-9642-0.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002A-5F9A-4 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-F769-2
Genre: Journal Article

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1603.08587.pdf (Preprint), 729KB
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 Creators:
Menne, U.1, Author              
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1Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_1753352              

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Free keywords: Mathematics, Differential Geometry, math.DG,Mathematics, Analysis of PDEs, math.AP,Mathematics, Classical Analysis and ODEs, math.CA,
 Abstract: The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that differentials are Borel functions, higher order rectifiability of the set of differentiability points, and a Rademacher result. One concept is characterised by a limit procedure involving inhomogeneously dilated sets. The original motivation to formulate the concepts stems from studying the support of stationary integral varifolds. In particular, strong pointwise differentiability of every positive integer order is shown at almost all points of the intersection of the support with a given plane.

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 Dates: 2016-03-2820162019
 Publication Status: Published online
 Pages: 33 pages
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 Identifiers: arXiv: 1603.08587
URI: http://arxiv.org/abs/1603.08587
DOI: 10.1007/s10455-018-9642-0
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Title: Annals of Global Analysis and Geometry
Source Genre: Journal
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