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

Marco Marchi — 2014

Annales de l’institut Fourier

In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ☆ ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type ☆ is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step...

Differentiability and Approximate Differentiability for Intrinsic Lipschitz Functions in Carnot Groups and a Rademacher Theorem

Bruno Franchi;  Marco Marchi;  Raul Paolo Serapioni — 2014

Analysis and Geometry in Metric Spaces

A Carnot group G is a connected, simply connected, nilpotent Lie group with stratified Lie algebra. We study intrinsic Lipschitz graphs and intrinsic differentiable graphs within Carnot groups. Both seem to be the natural analogues inside Carnot groups of the corresponding Euclidean notions. Here ‘natural’ is meant to stress that the intrinsic notions depend only on the structure of the algebra of G. We prove that one codimensional intrinsic Lipschitz graphs are sets with locally finite G-perimeter....

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