English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Pointwise differentiability of higher order for sets

MPS-Authors
/persons/resource/persons4295

Menne,  U.
Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)

1603.08587.pdf
(Preprint), 729KB

Supplementary Material (public)
There is no public supplementary material available
Citation

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


Cite as: http://hdl.handle.net/11858/00-001M-0000-002A-5F9A-4
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.