TY - JOUR
T1 - Dvoretzky-type theorem for Ahlfors regular spaces
AU - Mendel, Manor
N1 - Publisher Copyright:
© Instytut Matematyczny PAN, 2023.
PY - 2023
Y1 - 2023
N2 - It is proved that for any 0 < β < α, any bounded Ahlfors α-regular space contains a β-regular compact subset that embeds biLipschitzly in an ultrametric with distortion at most O(α/(α − β)). The bound on the distortion is asymptotically tight when β → α. The main tool used in the proof is a regular form of the ultrametric skeleton theorem.
AB - It is proved that for any 0 < β < α, any bounded Ahlfors α-regular space contains a β-regular compact subset that embeds biLipschitzly in an ultrametric with distortion at most O(α/(α − β)). The bound on the distortion is asymptotically tight when β → α. The main tool used in the proof is a regular form of the ultrametric skeleton theorem.
KW - Ahlfors regular spaces
KW - Dvoretzky-type theorems
KW - Hausdorff dimension
KW - biLipschitz embeddings
KW - metric Ramsey theory
KW - ultrametric skeleton
UR - http://www.scopus.com/inward/record.url?scp=85167975706&partnerID=8YFLogxK
U2 - 10.4064/sm210629-2-2
DO - 10.4064/sm210629-2-2
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AN - SCOPUS:85167975706
SN - 0039-3223
VL - 268
SP - 1
EP - 22
JO - Studia Mathematica
JF - Studia Mathematica
IS - 1
ER -