On Minkowski's Monotonicity Problem in Convex Geometry

Explore a mathematical physics lecture that delves into one of Minkowski's unresolved problems from his foundational work in convex geometry. Learn about recent progress on the equality characterization for the monotonicity of mixed volumes, presented by Princeton University's Ramon van Handel in collaboration with Shouda Wang. Gain insights into how this problem connects to Euler's classical observation about surfaces with vanishing Gaussian curvature being ruled surfaces, all explained from a geometric analysis perspective. Discover the historical significance of Minkowski's original paper from over 120 years ago and its continued influence on modern mathematics, including recent breakthroughs in the Alexandrov-Fenchel inequality's extremal characterization achieved with Yair Shenfeld. Engage with this complex mathematical topic through an accessible presentation that requires no prior background in convex geometry.