Riemannian Hessian analysis of Sobolev gradient flows for the Gross--Pitaevskii ground state problem

Sobolev gradient flows for the Gross--Pitaevskii ground state problem are Riemannian gradient descent methods on the sphere under a metric induced by a discrete elliptic operator. We analyze their convergence through the condition number of the Riemannian Hessian at the ground state. Bounds of the R