On a variational problem related to NLS on Hyperbolic space

TL;DR

This paper investigates a variational problem inspired by nonlinear Schrödinger equations on hyperbolic space, determining its minimum value and proving the non-existence of a minimizer.

Contribution

It provides the first analysis of a specific variational problem on hyperbolic space, including explicit computation of its minimum and non-existence of minimizers.

Findings

Computed the minimum value of the variational problem.

Proved that the minimizer does not exist.

Enhanced understanding of variational problems in hyperbolic geometry.

Abstract

Motivated by NLS, We study a variational problem on hyperbolic space. In particular, we compute its minimum value and we show the minimizer does not exist