Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds

TL;DR

This paper generalizes classical stability theorems for nonrelativistic hydrogen-like systems from Euclidean space to nonparabolic Riemannian 3-manifolds, broadening the mathematical understanding of quantum stability in curved spaces.

Contribution

It extends Euclidean stability results for one-electron ions to nonparabolic Riemannian 3-manifolds, introducing new geometric considerations into quantum stability analysis.

Findings

Stability theorems hold on nonparabolic manifolds

Extension of classical results to curved spaces

New techniques for quantum stability in geometric settings

Abstract

We extend classical Euclidean stability theorems corresponding to the nonrelativistic Hamiltonians of ions with one electron to the setting of non parabolic Riemannian 3-manifolds.