Calculus of Variations and Geometric Measure Theory
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B. Franchi - R. Serapioni - F. Serra Cassano

Intrinsic Lipshitz graphs in Heisenebrg groups

created by serracas on 18 Dec 2006


Accepted Paper

Inserted: 18 dec 2006

Journal: J. Nonlinear and Convex Analysis
Year: 2006


In this note we study the intrinsic Lipschitz functions acting between subgroups of the Heisenberg group $H^n$. One of our aims is convincing the reader that they are very natural objects inside $H^n$, enjoying a number of very natural properties: they can be defined equivalently by metric properties, boundedness of intrinsic difference quotients or existence of parallel cones non intersecting their graphs; their graphs have locally finite intrinsic Hausdorff measure and finally when they are $1$-codimensional they are boundary of sets with locally finite $H$-perimeter.


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