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math.MG2026
Flatness, Menger curvature, and parametrization
Guy C. David, Vyron Vellis
We show that on linearly locally contractible (LLC) manifolds, the beta numbers (which describe unilateral flatness) are comparable to the theta numbers (which describe bilateral f…
math.MG2025
The Heinonen-Semmes problems after thirty years
Guy C. David, Pekka Pankka, Jeremy T. Tyson
We survey the current status of the questions posed by Juha Heinonen and Stephen Semmes in `Thirty-three yes or no questions about mappings, measures, and metrics' (Conformal Geome…