On the fully nonlinear Yamabe problem with constant boundary mean curvature. I

TL;DR

This paper extends Liouville-type theorems for conformally invariant elliptic equations to the half-Euclidean space, advancing understanding of boundary value problems in geometric analysis.

Contribution

It provides the first optimal Liouville theorem for conformally invariant elliptic equations with boundary conditions in half-Euclidean space.

Findings

Established an optimal Liouville theorem in half-Euclidean space.

Extended previous Euclidean space results to boundary-involved settings.

Contributed to the theory of conformally invariant elliptic equations with boundary conditions.

Abstract

In a recent paper, we established optimal Liouville-type theorems for conformally invariant second-order elliptic equations in the Euclidean space. In this work, we prove an optimal Liouville-type theorem for these equations in the half-Euclidean space.