Directional Poincaré inequality on compact Lie groups
Abstract
We extend the directional Poincaré inequality on the torus, introduced by Steinerberger in [Ark. Mat. 54 (2016), pp. 555--569], to the setting of compact Lie groups. We provide necessary and sufficient conditions for the existence of such an inequality based on estimates on the eigenvalues of the global symbol of the corresponding vector field. We also prove that such refinement of the Poincaré inequality holds for a left-invariant vector field on a compact Lie group $G$ if and only if the vector field is globally solvable, and extend this equivalence to tube-type vector fields on $\mathbb{T}^1\times G$.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Nonlinear Partial Differential Equations
Advanced Harmonic Analysis Research
Publication details
- Journal / source
- Journal of Differential Equations
- Volume
- 461
- Pages
- 114109–114109
- Publication date
- 15 January 2026
- Language
- EN