Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schrödinger Operators of Finite Index

Hideaki Harumoto, Kei Kondo

In this article, we investigate the global topology of a complete non-compact Riemannian $2$-manifold $\Sigma$ admitting a Schrödinger operator with non-negative potential and finite Mo…