The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
Abstract We show that the β-numbers of intrinsic Lipschitz graphs of Heisenberg groups <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:msub><m:mi>ℍ</m:mi><m:mi>n</m:mi></m:msub></m:math> {\mathbb{H}_{n}} are locally Carleson integrable when <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"><m:mrow><m:mi>n</m:mi><m:mo>≥</m:mo><m:mn>2</m:mn></m:mrow></m:math> {n\geq 2} . Our main bound uses a novel slicing argument to decompose intrinsic Lipschitz graphs into graphs of Lipschitz functions. A key ingredient in our proof …