Research

Publications & Preprints

1. Synthetic Geometry in Hyperbolic Simplices  with Barry Minemyer.  Involve, a Journal of Mathematics. 15 (2023), Issue 5, 885-904. arXiv.

ABSTRACT: Let τ be an n-simplex and let g be a metric on τ with constant curvature κ. The lengths that g assigns to the edges of τ, along with the value of κ, uniquely determine all of the geometry of (τ,g). We focus on hyperbolic simplices (κ=−1) and develop geometric formulas which rely only on the edge lengths of τ. Our main results are distance and projection formulas in hyperbolic simplices, as well as a projection formula in Euclidean simplices. We also provide analogous formulas in simplices with arbitrary constant curvature κ.