Mass-Capacity Inequalities and Their Implications in Asymptotically Flat Manifolds

Explore the geometric invariant of mass in asymptotically flat manifolds and its implications in this 1-hour 5-minute conference talk by Pengzi Miao at ICBS2024. Delve into the Riemannian positive mass theorem and its significance for manifolds with nonnegative scalar curvature. Examine the Riemannian Penrose inequality, which provides a sharp lower bound for mass in relation to the area of outer minimizing surfaces. Discover new sharp inequalities connecting mass to the capacity of boundary surfaces, and investigate their practical applications in the field of general relativity and geometric analysis.