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A Sharp Isoperimetric-Type Inequality for Lorentzian Spaces Satisfying Time-Like Ricci Curvature Lower Bounds

Offered By: Erwin Schrödinger International Institute for Mathematics and Physics (ESI) via YouTube

Tags

Isoperimetric Inequalities Courses Cosmology Courses Black Holes Courses Optimal Transport Courses Ricci Curvature Courses Lorentzian Geometry Courses Synthetic Geometry Courses

Course Description

Overview

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Explore a cutting-edge seminar on Lorentzian geometry and synthetic curvature bounds presented at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into recent joint research establishing a sharp and rigid isoperimetric-type inequality in Lorentzian signature under time-like Ricci curvature lower bounds. Discover how this groundbreaking work applies to both smooth Lorentzian manifolds and more general Lorentzian length spaces using optimal transport techniques. Examine fascinating applications, including upper area bounds for Cauchy hypersurfaces within black hole interiors and cosmological space-times. Gain insights into the intersection of differential geometry, general relativity, and optimal transport theory in this 49-minute talk from the Workshop on "Synthetic Curvature Bounds for Non-Smooth Spaces: Beyond Finite Dimension."

Syllabus

Andrea Mondino - A sharp isoperimetric-type inequality for Lorentzian spaces satisfying time-like...


Taught by

Erwin Schrödinger International Institute for Mathematics and Physics (ESI)

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