EAN: 9783030552923

ADVANCED COURSES IN MATHEMATICS - CRM BARCELONA...

This book contains a clear exposition of two contemporary topics in modern differential
geometry: distance geometric analysis on manifolds  in particular  comparison theory for
distance functions in spaces which have well defined bounds on their curvature the study of
scalar curvature rigidity and positive mass theorems using spinors and the Dirac operator It is
intended for both graduate students and researchers. This second edition has been updated to
include recent developments such as promising results concerning the geometry of exit time
moment spectra and potential analysis in weighted Riemannian manifolds  as well as results
pertaining to an early conjecture on the geometry of the scalar curvature and speculations on
new geometric approaches to the Index Theorem.

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