Regularity of sets with constant intrinsic normal in a class of Carnot\n groups

2012/01/16 by Marco Marchi, Marchi, Marco · 1 citation
Mathematics · #28A75 (Primary) 49Q15 #58C35 (Secondary) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG)

paper · pdf · doi:10.48550/arxiv.1201.3277

openalex publication_date 2012/01/16 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

In this Note, we define a class of stratified Lie groups of arbitrary step\n(that are called ``groups of type \⋆'' throughout the paper), and we prove\nthat, in these groups, sets with constant intrinsic normal are vertical\nhalfspaces. As a consequence, the reduced boundary of a set of finite intrinsic\nperimeter in a group of type \⋆ is rectifiable in the intrinsic sense (De\nGiorgi's rectifiability theorem). This result extends the previous one proved\nby Franchi, Serapioni & Serra Cassano in step 2 groups.\n

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