Oberwolfach Workshop Report: Analysis, Geometry and Topology of Positive Scalar Curvature Metrcs: Limits of sequences of manifolds with nonnegative scalar curvature and other hypotheses

TL;DR

This report surveys sequences of manifolds with nonnegative scalar curvature, discusses convergence results, and presents open questions, highlighting recent progress and future directions in geometric analysis.

Contribution

It provides a comprehensive survey of examples and convergence results for manifolds with nonnegative scalar curvature, including an extreme example and open problems.

Findings

Convergence of sequences with nonnegative scalar curvature

An extreme example illustrating limits of such sequences

Open questions guiding future research in scalar curvature geometry

Abstract

This report contains a survey of examples of sequences of manifolds with nonnegative scalar curvature including an extreme example with Wenchuan Tian and Changliang Wang. It announces a paper with Wenchaun Tian proving the GH and SWIF convergence of the extreme example. It contains six Open Questions concerning such sequences.