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- W1989474511 abstract "We establish an explicit formula between the perimeter measure of an open set $E$ with $C^1$ boundary and the spherical Hausdorff measure $cS^{Q-1}$ restricted to $der E$, when the ambient space is a stratified group endowed with a left invariant sub-Riemannian metric and $Q$ denotes the Hausdorff dimension of the group. Our formula implies that the perimeter measure of $E$ is less than or equal to $cS^{Q-1}(der E)$ up to a dimensional factor. The validity of this estimate positively answers a conjecture raised by Danielli, Garofalo and Nhieu. The crucial ingredient of this result is the negligibility of ``characte-ristic points of the boundary. We introduce the notion of ``horizontal point, which extends the notion of characteristic point to arbitrary submanifolds and we prove that the set of horizontal points of a $k$-codimensional submanifold is $cS^{Q-k}$-negligible. We propose an intrinsic notion of rectifiability for subsets of higher codimension, namely, $(G,R^k)$-rectifiability and we prove that Euclidean $k$-codimensional rectifiable sets are $(G,R^k)$-rectifiable." @default.
- W1989474511 created "2016-06-24" @default.
- W1989474511 creator A5047016245 @default.
- W1989474511 date "2006-01-01" @default.
- W1989474511 modified "2023-09-30" @default.
- W1989474511 title "Characteristic points, rectifiability and perimeter measure on stratified groups" @default.
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- W1989474511 doi "https://doi.org/10.4171/jems/68" @default.
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