Ultrametric subsets with large Hausdorff dimension

Manor Mendel, Assaf Naor

نتاج البحث: نشر في مجلةمقالةمراجعة النظراء


It is shown that for every ε∈(0,1), every compact metric space (X,d) has a compact subset S⊆X that embeds into an ultrametric space with distortion O(1/ε), and dimH(S),≥(1-ε)dimH(X) where dimH(·) denotes Hausdorff dimension. The above O(1/ε) distortion estimate is shown to be sharp via a construction based on sequences of expander graphs.

اللغة الأصليةالإنجليزيّة
الصفحات (من إلى)1-54
عدد الصفحات54
دوريةInventiones Mathematicae
مستوى الصوت192
رقم الإصدار1
المعرِّفات الرقمية للأشياء
حالة النشرنُشِر - أبريل 2013

ملاحظة ببليوغرافية

Funding Information:
M.M. was partially supported by ISF grants 221/07 and 93/11, BSF grants 2006009 and 2010021, and a gift from Cisco Research Center. A.N. was partially supported by NSF grant CCF-0832795, BSF grants 2006009 and 2010021, and the Packard Foundation. Part of this work was completed when M.M. was visiting Microsoft Research and University of Washington, and A.N. was visiting the Discrete Analysis program at the Isaac Newton Institute for Mathematical Sciences and the Quantitative Geometry program at the Mathematical Sciences Research Institute.


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