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Regular orbital measures on Lie algebras

Alex Wright (2008)

Colloquium Mathematicae

Let H₀ be a regular element of an irreducible Lie algebra , and let μ H ₀ be the orbital measure supported on O H ₀ . We show that μ ̂ H ₀ k ∈ L ² ( ) if and only if k > dim /(dim - rank ).

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...

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