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.

  Discussion of the Laplacian as a 'swift' operator on minimal submanifolds in ambient spaces with small sectional curvatures Use of Dirac operators for general relativity Contains a clear exposition of contemporary topics in modern differential geometry

  Autorentext

  Ana Hurtado is a professor at the Universidad de Granada. Steen Markvorsen is a professor at the Technical University of Denmark. Maung Min-Oo is emeritus professor at the McMaster University. Vicente Palmer is a professor of Geometry at the University Jaume I.

  Inhalt
  Distance Geometric Analysis on Manifolds.- The Dirac Operator in Geometry and Physics.