The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg\n groups

2020/04/23 by Vasileios Chousionis, Sean Li, Chousionis, Vasileios +3 · 1 citation
Mathematics · #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.11447

Abstract

We show that the \β--numbers of intrinsic Lipschitz graphs of Heisenberg\ngroups \ℍ_n are locally Carleson integrable when n \≥ 2. Our\ntechnique relies on a recent Dorronsoro inequality citeFO as well as a novel\nslicing argument. A key ingredient in our proof is a Euclidean inequality\nbounding the \β--number of a function on a cube of \ℝⁿ using\nthe \β--number of the restriction of the function to codimension--1 slices\nof the cube.\n

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• On Singular Integrals and Quantitative Rectifiability in Parabolic Space and the Heisenberg Group

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