6533b7dcfe1ef96bd1271e3d

RESEARCH PRODUCT

Nowhere differentiable intrinsic Lipschitz graphs

Davide VittoneAntoine JuliaSebastiano Nicolussi Golo

subject

Pure mathematicsProperty (philosophy)General MathematicsMathematics::Analysis of PDEs01 natural sciencesdifferentiaaligeometriasymbols.namesakeMathematics - Metric Geometry0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: MathematicsMathematics::Metric GeometryPoint (geometry)Differentiable function0101 mathematicsMathematics010102 general mathematicsryhmäteoriaMetric Geometry (math.MG)16. Peace & justiceLipschitz continuity53C17 58C20 22E25Mathematics - Classical Analysis and ODEsHomogeneoussymbols010307 mathematical physicsCarnot cycleCounterexample

description

We construct intrinsic Lipschitz graphs in Carnot groups with the property that, at every point, there exist infinitely many different blow-up limits, none of which is a homogeneous subgroup. This provides counterexamples to a Rademacher theorem for intrinsic Lipschitz graphs.

yearjournalcountryeditionlanguage
2021-01-08
https://dx.doi.org/10.48550/arxiv.2101.02985