We introduce the notion of ”metric normal” to a surface in the Heisenberg group H, which extends in a metric way the notion of segment normal to a surface in Euclidean space. We use this notion to prove regularity results for the function dS measuring the Carnot distance from a surface S in H. An explicit expression for the horizontal Hessian of dS and of the Carnot distance itself is computed. (Received September 11, 2006).
N. Arcozzi, F. Ferrari (2006). The Hessian of the distance function in the Heisenberg group.. s.l : AMS.
The Hessian of the distance function in the Heisenberg group.
ARCOZZI, NICOLA;FERRARI, FAUSTO
2006
Abstract
We introduce the notion of ”metric normal” to a surface in the Heisenberg group H, which extends in a metric way the notion of segment normal to a surface in Euclidean space. We use this notion to prove regularity results for the function dS measuring the Carnot distance from a surface S in H. An explicit expression for the horizontal Hessian of dS and of the Carnot distance itself is computed. (Received September 11, 2006).File in questo prodotto:
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