On the Scalar Compactness Conjecture in the Conformal Case

Abstract: Understanding in what sense scalar curvature is flexible versus rigid has been an important area of investigation in geometric analysis. We have many rigidity phenomena involving scalar curvature understood and we are recently turning to the question of stability. One question in this direction asks, If we take a sequence of Riemannian manifolds with non-negative scalar curvature, then what additional hypotheses need to be added to ensure that a subsequence exists which converges to a metric space with some notion of weakly non-negative scalar curvature? In this talk we will investigate this question in the case where the sequence of Riemannian manifolds is conformal to the round sphere.

Mathematics

Audience: researchers in the topic

IUT Mathematics Research Seminars (IMRS)

Series comments: All researchers are welcomed!