Positive Mass Theorem for Asymptotically Flat Manifolds with Isolated Conical Singularities

Explore a 45-minute lecture on the positive mass theorem for asymptotically flat manifolds with isolated conical singularities. Delve into recent joint works by Changliang Wang, Xianzhe Dai, and Yukai Sun as they extend Witten's argument in the spin setting and apply conformal blow-up techniques in the non-spin setting. Examine the solutions to the Dirac operator and Laplace equation on asymptotically flat manifolds with conical singularities. Investigate the rigidity result through partial asymptotic expansion of solutions. Learn how the analysis of conically singular manifolds, combined with conformal blow-up techniques and generalized Geroch-type results, leads to a Geroch-type result for isolated conical singularities. Gain insights from Changliang Wang of Tongji University in this scientific presentation available on CARMIN.tv, a French video platform offering specialized content for the mathematics research community.