We study the notion of intrinsic Lipschitz graphs within Heisenberg groups, focusing our attention on their Hausdorff dimension and on almost everywhere existence of (geometrically defined) tangent subgroups. In particular, a Rademacher type theorem enables us to prove that previous definitions of rectifiable sets in Heisenberg groups are natural ones.
B. Franchi, R. Serapioni, F. Serra Cassano (2011). Differentiability of intrinsic Lipschitz functions within Heisenberg groups. THE JOURNAL OF GEOMETRIC ANALYSIS, 21, 1044-1084 [10.1007/s12220-010-9178-4].
Differentiability of intrinsic Lipschitz functions within Heisenberg groups
FRANCHI, BRUNO;
2011
Abstract
We study the notion of intrinsic Lipschitz graphs within Heisenberg groups, focusing our attention on their Hausdorff dimension and on almost everywhere existence of (geometrically defined) tangent subgroups. In particular, a Rademacher type theorem enables us to prove that previous definitions of rectifiable sets in Heisenberg groups are natural ones.File in questo prodotto:
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