On the Gromov–Hausdorff stability of metric viscosity solutions
Abstract
We establish the stability of metric viscosity solutions to first-order Hamilton–Jacobi equations under Gromov–Hausdorff convergence. Our proof combines a characterization of metric viscosity solutions via quadratic distance functions with a doubling variable method adapted to ϵ \epsilon -isometries, which allows us to pass to the Gromov–Hausdorff limit without embedding the spaces into a common ambient space. As a byproduct, we give a PDE-based proof of the stability of the dual Kantorovich problems under measured-Gromov–Hausdorff convergence.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Optimization and Variational Analysis
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 4
- Pages
- 1701–1714
- Publication date
- 10 February 2026
- Language
- EN