Hideaki Harumoto

Curvature at Infinity Governs the Topology of Complete Non-Compact Surfaces Admitting Schr\"odinger Operators of Finite Index

In this article, we investigate the global topology of a complete non-compact Riemannian $2$-manifold $\Sigma$ admitting a Schr\"odinger operator with non-negative potential and finite Morse index. While classical results of Fischer-Colbrie classify such manifolds under the assumption of vanishing index or geometric st...