Work

Hausdorff stability of the cut locus under C2-perturbations of the metric

Year: 2025

Type: article

Abstract: In this article, we prove the stability with respect to the Hausdorff metric d H of the cut locus Cut ( p , g ) of a point p in a compact Riemannian manifold ( M , g ) under C 2 perturbation of the metric. Specifically, given a sequence of metrics g i on M , converging to g in the C 2 topology, and a sequence of points p i in M , converging to p , we show that lim i ⁡ d H ( Cut ( p i , g i ) , Cut ( p , g ) ) = 0 . Along the way, we also prove the continuous dependence of the cut time map on the metric.

Source: Journal of Mathematical Analysis and Applications

DOI: 10.1016/j.jmaa.2025.130324

Authors: Aritra Bhowmick, Jin-ichi Itoh, Sachchidanand Prasad

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Jilin University, National Board for Higher Mathematics, Japan Society for the Promotion of Science

Awards: G3407218169, New applications of cut loci and problems related to geodesics, G8446196519