Perspectives in scalar curvature Mikhail L Gromov and H Blaine Lawson eds.

Includes bibliography and index

Vol 1:
Four lecture on Scalar Curvature -- Scalar curvature and generalized callias operators -- Convergence and regularity of manifolds with scalar curvature and entropy lower bounds -- level set methods in the study of scalar curvature -- The secret hyperbolic life of positive scalar curvature -- The scalar curvature of 4-Manifolds

This volume contains a long article by Misha Gromov based on his many years of involvement in this subject. It came from lectures delivered in Spring 2019 at IHES. There is some background given. Many topics in the field are presented, and many open problems are discussed. One intriguing point here is the crucial role played by two seemingly unrelated analytic means: index theory of Dirac operators and geometric measure theory.Very recently there have been some real breakthroughs in the field. Volume I has several survey articles written by people who were responsible for these results.For Volume II, many people in areas of mathematics and physics, whose work is somehow related to scalar curvature, were asked to write about this in any way they pleased. This gives rise to a wonderful collection of articles, some with very broad and historical views, others which discussed specific fascinating subjects.These two books give a rich and powerful view of one of geometry's very appealing sides.