PreprintarXiv licencearXiv
Electrostatic inequalities and stability of matter on asymptotically Euclidean manifolds
Abstract
We prove stability of nonrelativistic fermionic matter in the presence of fixed nuclei {Rj} on an asymptotically Euclidean Riemannian manifold (M,g). Upper and lower bounds on sectional curvatures are assumed, but no specific sign conditions on the curvature are imposed. The proof follows the route of Lieb-Thirring and electrostatic inequalities, the latter being proved by means of a Voronoi decomposition type argument which is however based on the Green functions {G( · ,Rj)} rather than the distance function.
Related
- Sharp L2-stability and gradient stability hierarchies of the L2-Poincaré inequalities on Euclidean balls and Gaussian Poincaré inequality
- Positive mass theorems for singular asymptotically hyperbolic manifolds
- A new boundary mass for asymptotically flat half-manifolds
- Convex hulls and area minimizing currents in asymptotically locally hyperbolic manifolds
- Isometric Embeddings of Asymptotically Hyperbolic Manifolds into Hyperbolic Space
BibTeX
@misc{stuart2026electrostatic,
title = {{Electrostatic inequalities and stability of matter on asymptotically Euclidean manifolds}},
author = {David Stuart},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06624},
eprint = {2610.06624},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06624},
}
RIS
TY - UNPB
TI - Electrostatic inequalities and stability of matter on asymptotically Euclidean manifolds
AU - David Stuart
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.06624
UR - https://arxiv.org/abs/2610.06624
AB - We prove stability of nonrelativistic fermionic matter in the presence of fixed nuclei {R_j} on an asymptotically Euclidean Riemannian manifold (M,g). Upper and lower bounds on sectional curvatures are assumed, but no specific sign conditions on the curvature are imposed. The proof follows the route of Lieb-Thirring and electrostatic inequalities, the latter being proved by means of a Voronoi decomposition type argument which is however based on the Green functions {G( · ,R_j)} rather than the distance function.
ER -