Geodesic
Wild examples of countably rectifiable sets
Max Goering1 ; Sean McCurdy2
1 University of Washington, Department of Mathematics
2 Carnegie Mellon University, Department of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 553-570.

Voir la notice de l'article provenant de la source Journal.fi

We study the geometry of sets based on the behavior of the Jones function, $J_{E}(x) = \int_{0}^{1} \beta_{E;2}^{1}(x,r)^{2} \frac{dr}{r}$. We construct two examples of countably 1-rectifiable sets in $\mathbf{R}^{2}$ with positive and finite $\mathcal{H}^1$-measure for which the Jones function is nowhere locally integrable. These examples satisfy different regularity properties: one is connected and one is Ahlfors regular. Both examples can be generalized to higher-dimension and co-dimension.
Keywords: Jones square function, rectifiability, traveling salesman, beta numbers

Max Goering 1 ; Sean McCurdy 2

1 University of Washington, Department of Mathematics
2 Carnegie Mellon University, Department of Mathematics 
@article{AFM_2021_46_1_a32,
     author = {Max Goering and Sean McCurdy},
     title = {Wild examples of countably rectifiable sets},
     journal = {Annales Fennici Mathematici},
     pages = {553--570},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a32/}
}
TY  - JOUR
AU  - Max Goering
AU  - Sean McCurdy
TI  - Wild examples of countably rectifiable sets
JO  - Annales Fennici Mathematici
PY  - 2021
SP  - 553
EP  - 570
VL  - 46
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a32/
LA  - en
ID  - AFM_2021_46_1_a32
ER  - 
%0 Journal Article
%A Max Goering
%A Sean McCurdy
%T Wild examples of countably rectifiable sets
%J Annales Fennici Mathematici
%D 2021
%P 553-570
%V 46
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a32/
%G en
%F AFM_2021_46_1_a32
Max Goering; Sean McCurdy. Wild examples of countably rectifiable sets. Annales Fennici Mathematici, Tome 46 (2021) no. 1, pp. 553-570. http://geodesic.mathdoc.fr/item/AFM_2021_46_1_a32/