In this talk, we will discuss two types of curvature-like inequalities: the short diagonals inequality for uniform convexity and the fork inequality.
These inequalities can be carefully iterated to produce metric invariants that capture the geometry of 2-branching diamond graphs and binary trees, respectively.
These metric invariants provide quantitative information about the distortion of bi-Lipschitz embeddings and the compression rate of coarse embeddings of the graphs above. We will study the validity of these curvature-like inequalities in Heisenberg groups over Banach spaces.
If time permits, we will also discuss asymptotic analogs of these inequalities. No prior knowledge about sub-Riemannian geometry is needed to follow the talk.
joint work with C. Gartland (UC San Diego).
