In Rdbld we consider a Riemannian metric, g, and an open bounded subset, Ω. We study the stability of the cut locus associated with Ω and g w.r.t. perturbations both of the set Ω and of the metric g. In order to have the stability of the cut locus, we assume C2 regularity of the data, the metrics and the sets (in the case of sets with C1,1 boundaries, the cut locus may be unstable). We prove that to C2 perturbations both of the set and of the metric correspond small changes of the cut locus w.r.t. the Hausdorff distance, i.e. the cut locus is stable in the C2 category. We give some examples showing that C1 perturbations may lead to large variations of the cut locus.
Albano, P. (2016). On the stability of the cut locus. NONLINEAR ANALYSIS, 136, 51-61 [10.1016/j.na.2016.02.008].
On the stability of the cut locus
ALBANO, PAOLO
2016
Abstract
In Rdbld we consider a Riemannian metric, g, and an open bounded subset, Ω. We study the stability of the cut locus associated with Ω and g w.r.t. perturbations both of the set Ω and of the metric g. In order to have the stability of the cut locus, we assume C2 regularity of the data, the metrics and the sets (in the case of sets with C1,1 boundaries, the cut locus may be unstable). We prove that to C2 perturbations both of the set and of the metric correspond small changes of the cut locus w.r.t. the Hausdorff distance, i.e. the cut locus is stable in the C2 category. We give some examples showing that C1 perturbations may lead to large variations of the cut locus.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
