Liouville theorem for k -curvature equation in half space with fully nonlinear boundary condition
Abstract
Abstract We establish the Liouville theorem for positive constant σ k {\sigma_{k}} -curvature equation in ℝ + n {\mathbb{R}_{+}^{n}} and positive constant boundary ℬ k g {\mathcal{B}_{k}^{g}} curvature equation, where the boundary curvature ℬ k g {\mathcal{B}_{k}^{g}} is discovered by Sophie Chen in [S.-Y. S. Chen, Conformal deformation on manifolds with boundary, Geom. Funct. Anal. 19 2009, 4, 1029–1064] from the natural variational functional for σ k ( A g ) {\sigma_{k}(A_{g})} .
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Advances in Calculus of Variations
- Publisher
- Walter de Gruyter GmbH
- Volume
- 19
- Issue
- 2
- Pages
- 179–195
- Publication date
- 13 January 2026
- Language
- EN