Calculus of Variations and Geometric Measure Theory
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G. Arena - A. O. Caruso - R. Monti

"Regularity properties of $H$--convex sets"

created by arena on 21 May 2010
modified by monti on 10 Sep 2010


Accepted Paper

Inserted: 21 may 2010
Last Updated: 10 sep 2010

Journal: J. Geom. Analysis
Year: 2010


We study the first- and second-order regularity properties of the boundary of $H$--convex sets in the setting of a real vector space endowed with a suitable group structure: our starting point is indeed a step two Carnot group. We prove that, locally, the noncharacteristic part of the boundary has the intrinsic cone property and that it is foliated by intrinsic Lipschitz continous curves that are twice differentiable almost everywhere.


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