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 application of the Lichnerowicz formula for Dirac operators to the study of Gromov's invariants to measure the K-theoretic size of a Riemannian manifold.
It is intended for both graduate students and researchers.
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.
Distance Geometric Analysis on Manifolds (Steen Markvorsen) .- The Dirac Operator in Geometry and Physics (Maung Min-Oo)