A fully nonlinear version of the Yamabe problem on locally conformally flat manifolds with umbilic boundary

TL;DR

This paper proves the existence and compactness of solutions for a fully nonlinear Yamabe problem on locally conformally flat manifolds with umbilic boundary, extending classical results to a more general nonlinear setting.

Contribution

It introduces a fully nonlinear approach to the Yamabe problem on manifolds with boundary, establishing existence and compactness results in this broader context.

Findings

Existence of solutions for the nonlinear Yamabe problem.

Compactness of the solution set.

Extension of classical Yamabe results to fully nonlinear cases.

Abstract

In this paper we establish existence and compactness of solutions to a general fully nonlinear version of the Yamabe problem on locally conformally flat Riemannian manifolds with umbilic boundary.