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).
The Hessian of the distance function in the Heisenberg group / N. Arcozzi; F. Ferrari. - ELETTRONICO. - (2006). (Intervento presentato al convegno 2006 Fall Southeastern Section Meeting of the AMS Meeting #1022 tenutosi a Fayetteville, AR, nel November 3-4, 2006 (Friday - Saturday)).
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).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.