Hyperbolic Summation and Hyperbolic Convex Geometry

Explore the development of hyperbolic convex geometry through a novel approach to set summation in hyperbolic space in this 47-minute mathematical lecture. Learn about the historical foundations of convex geometry in Euclidean space, beginning with H. Brunn's 1887 thesis and H. Minkowski's 1903 paper on Minkowski summation. Discover how the speaker introduces a new concept called "hyperbolic summation" for sets in hyperbolic space, which serves as the foundation for developing an entirely new framework of hyperbolic convex geometry. Gain insights into this collaborative research conducted with Dr. Botong Xu, which extends classical geometric concepts into the hyperbolic setting and opens new avenues for mathematical exploration in non-Euclidean spaces.