Failure of the Curvature-Dimension Condition in Sub-Finsler Manifolds

Explore the failure of the Lott-Sturm-Villani CD(K,N) condition in sub-Finsler manifolds during this 40-minute conference talk from the Workshop on "Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into recent findings that demonstrate the CD condition's invalidity in sub-Riemannian manifolds with positive smooth measures, regardless of parameter choices. Examine two key results: the failure of the CD condition in sub-Finsler manifolds with smooth strongly convex norms and positive smooth measures, and its failure in the sub-Finsler Heisenberg group for all reference norms. Additionally, investigate how the measure contraction property MCP(K,N) in the sub-Finsler Heisenberg group depends on the regularity of the reference norm.