Penrose-Almost -Rigidity-Geometrostatic

Scalar Curvature and Intrinsic Flat Convergence - Prof. Sormani

Fields Institute Summer School on Geometric Analysis

Almost Rigidity* of the Penrose Inequality in the Geometrostatic Setting Project (p 74 of course notes)

This team now meets periodically on Friday mornings via skype.

Shubham and Rohit came to the Montreal meeting and Tobias skyped in.

*Warning: The term "almost rigidity theorem" was introduced by Cheeger-Colding in their 1996 paper. In these lectures, I used the term more generally including theorems that they would call "stability theorems". Indeed Gromov also states his conjectures as "stability conjectures". I avoided the use of the word "stability" in my lectures due to confusions arising with other usages of the word stability when dealing with manifolds that have scalar curvature bounds. In April 2018, Jeff Cheeger requested that we not use the term "almost rigidity" in this new expanded way but only use it to refer to theorems in which the limit space is not predetermined (as explained in their original paper). Although the conjectures stated here and various teams listed above use the term "almost rigidity" it is best to publish your results using the term "stability" or just simply state the theorems without naming them.

Sormani was partially supported by NSF DMS \#1006059