scholarly journals On the distance sets of Ahlfors–David regular sets

2017 ◽  
Vol 307 ◽  
pp. 1029-1045 ◽  
Author(s):  
Tuomas Orponen
Keyword(s):  
Regular Sets ◽  
Distance Sets

scholarly journals Prox-regular sets and Legendre-Fenchel transform related to separation properties

Optimization ◽  
2020 ◽  
pp. 1-33
Author(s):  
Samir Adly ◽  
Florent Nacry ◽  
Lionel Thibault
Keyword(s):  
Fenchel Transform ◽  
Regular Sets

scholarly journals Plenty of big projections imply big pieces of Lipschitz graphs

2021 ◽  
Author(s):  
Tuomas Orponen
Keyword(s):  
Lipschitz Graphs ◽  
Regular Sets ◽  
Big Pieces

AbstractI prove that closed n-regular sets $$E \subset {\mathbb {R}}^{d}$$ E ⊂ R d with plenty of big projections have big pieces of Lipschitz graphs. In particular, these sets are uniformly n-rectifiable. This answers a question of David and Semmes from 1993.

On the Hausdorff dimensions of distance sets

Mathematika ◽  
1985 ◽  
Vol 32 (2) ◽  
pp. 206-212 ◽  
Author(s):  
K. J. Falconer
Keyword(s):  
Hausdorff Dimensions ◽  
Distance Sets

Hausdorff dimension and distance sets

1994 ◽  
Vol 87 (1-3) ◽  
pp. 193-201 ◽  
Author(s):  
Jean Bourgain
Keyword(s):  
Hausdorff Dimension ◽  
Distance Sets

Equational axioms for regular sets

1993 ◽  
Vol 3 (1) ◽  
pp. 1-24 ◽  
Author(s):  
S. L. Bloom ◽  
Z. Ésik
Keyword(s):  
Star Operation ◽  
Regular Sets

We show that, aside from the semiring equations, three equations and two equation schemes characterize the semiring of regular sets with the Kleene star operation.

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