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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…
math.CA2025
An existence theorem for sliding minimal sets
Guy David, Camille Labourie
We prove an existence theorem for the sliding boundary variant of the Plateau problem for -dimensional sets in . The simplest case of sufficient condition is when…
math.CA2025
Coarse and pointwise tangent fields
Guy C. David, Sylvester Eriksson-Bique, Raanan Schul
Alberti, Csörnyei and Preiss introduced a notion of a "pointwise (weak) tangent field" for a subset of Euclidean space -- a field that contains almost every tangent line of every c…