Lipschitz functions on submanifolds in Heisenberg groups

Abstract

We study the behavior of Lipschitz functions on intrinsic C 1 submanifolds of Heisenberg groups: our main result is their almost everywhere tangential Pansu differentiability. We also provide two applications: a Lusintype approximation of Lipschitz functions on H-rectifiable sets, and a coarea formula on H-rectifiable sets that completes the program started in [16]. ContentsContents 1 1. Introduction 1 2. Preliminaries 4 3. Pansu differentiability on C 1 H submanifolds 8 4. Proof of Theorem A 9 5. Proof of Theorem B 13 6. Proof of Theorem C 14 References 15

Rectifiability; a survey

“…Counter-examples to Rademacher's theorem for intrinsic Lipschitz graphs in some Carnot groups were given by Julia, Nicolussi Golo and Vittone in [JNV21a]. In [JNV21b] they proved the almost everywhere tangential differentiability of Euclidean valued functions on C 1 H submanifolds of H n yielding on H-rectifiable sets a Lusin type approximation of Lipschitz functions and a coarea formula.…”