Webrelaunch 2020

AG Stochastische Geometrie am 16.11.2009

Amos Koeller: On the regularity of sets with varying Reifenberg conditions

Variants of Reifenberg's 1960 defined affine approximation of sets in
Euclidean spaces have recently found application in various mathematical
contexts; including infinity-harmonic funcions, BV functions and minimal
surface theory. Reifenberg sets can be, however, extremely irregular,
having, in some cases, a different Hausdorff dimension to that expected.
We classify the variants of Reifenberg's definition with respect to what
level of regularity they imply. That is, whether a Reifenberg set has the
expected Hausdorff dimension, finite Hausdorff measure or is countably
rectifiable. This classification can be further extended to the notions of
Packing measure as well as Packing and Minkowski dimensions. In some cases
the regularity of a graphical representation may also be considered.