Cherrier–Escobar problem for the elliptic Schrödinger-to-Neumann map

Abstract

In this paper, we study a Cherrier–Escobar problem for the extended problem corresponding to the elliptic Schrödinger-to-Neumann map on a compact 3-dimensional Riemannian manifold with boundary. Using the algebraic topological argument of Bahri and Coron (1988), we show solvability under the assumption that the extended problem corresponding to the elliptic Schrödinger-to-Neumann map has a positive first eigenvalue and a positive Green’s function.