Geodesic
ON GILP’S GROUP-THEORETIC APPROACH TO FALCONER’S DISTANCE PROBLEM
Glasgow mathematical journal, Tome 63 (2021) no. 3, pp. 547-562

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DOI

In this paper, we follow and extend a group-theoretic method introduced by Greenleaf–Iosevich–Liu–Palsson (GILP) to study finite points configurations spanned by Borel sets in $\mathbb{R}^n,n\geq 2,n\in\mathbb{N}.$ We remove a technical continuity condition in a GILP’s theorem in [Revista Mat. Iberoamer 31 (2015), 799–810]. This allows us to extend the Wolff–Erdogan dimension bound for distance sets to finite points configurations with k points for $k\in\{2,\dots,n+1\}$ forming a $(k-1)$ -simplex. 
YU, HAN. ON GILP’S GROUP-THEORETIC APPROACH TO FALCONER’S DISTANCE PROBLEM. Glasgow mathematical journal, Tome 63 (2021) no. 3, pp. 547-562. doi: 10.1017/S0017089520000373
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     title = {ON {GILP{\textquoteright}S} {GROUP-THEORETIC} {APPROACH} {TO} {FALCONER{\textquoteright}S} {DISTANCE} {PROBLEM}},
     journal = {Glasgow mathematical journal},
     pages = {547--562},
     year = {2021},
     volume = {63},
     number = {3},
     doi = {10.1017/S0017089520000373},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089520000373/}
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