TY - JOUR

T1 - Pointwise differentiability of higher order for sets

AU - Menne, Ulrich

N1 - Publisher Copyright:
© 2019, Springer Nature B.V.

PY - 2019/4/1

Y1 - 2019/4/1

N2 - 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.

AB - 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.

KW - Higher-order pointwise differentiability

KW - Rademacher–Stepanov type theorem

KW - Rectifiability

KW - Stationary integral varifold

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U2 - 10.1007/s10455-018-9642-0

DO - 10.1007/s10455-018-9642-0

M3 - Article

AN - SCOPUS:85060063242

SN - 0232-704X

VL - 55

SP - 591

EP - 621

JO - Annals of Global Analysis and Geometry

JF - Annals of Global Analysis and Geometry

IS - 3

ER -