Riemannian Geometry And Geometric Analysis (universitext)
by Jürgen Jost /
2017 / English / PDF
16 MB Download
This established reference work continues to provide its
readers with a gateway to some of the most interesting
developments in contemporary geometry. It offers insight into a
wide range of topics, including fundamental concepts of
Riemannian geometry, such as geodesics, connections and
curvature; the basic models and tools of geometric analysis,
such as harmonic functions, forms, mappings, eigenvalues, the
Dirac operator and the heat flow method; as well as the most
important variational principles of theoretical physics, such
as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of
quantum field theory. The present volume connects all these
topics in a systematic geometric framework. At the same time,
it equips the reader with the working tools of the field and
enables her or him to delve into geometric research.
This established reference work continues to provide its
readers with a gateway to some of the most interesting
developments in contemporary geometry. It offers insight into a
wide range of topics, including fundamental concepts of
Riemannian geometry, such as geodesics, connections and
curvature; the basic models and tools of geometric analysis,
such as harmonic functions, forms, mappings, eigenvalues, the
Dirac operator and the heat flow method; as well as the most
important variational principles of theoretical physics, such
as Yang-Mills, Ginzburg-Landau or the nonlinear sigma model of
quantum field theory. The present volume connects all these
topics in a systematic geometric framework. At the same time,
it equips the reader with the working tools of the field and
enables her or him to delve into geometric research.
The 7th edition has been systematically reorganized and
updated. Almost no page has been left unchanged. It also
includes new material, for instance on symplectic geometry, as
well as the Bishop-Gromov volume growth theorem which
elucidates the geometric role of Ricci curvature.
The 7th edition has been systematically reorganized and
updated. Almost no page has been left unchanged. It also
includes new material, for instance on symplectic geometry, as
well as the Bishop-Gromov volume growth theorem which
elucidates the geometric role of Ricci curvature.From the reviews:
From the reviews:
“This book provides a very readable introduction to
Riemannian geometry and geometric analysis... With the vast
development of the mathematical subject of geometric
analysis, the present textbook is most
welcome.”
“This book provides a very readable introduction to
Riemannian geometry and geometric analysis... With the vast
development of the mathematical subject of geometric
analysis, the present textbook is most
welcome.”Mathematical Reviews
Mathematical Reviews
“For readers familiar with the basics of differential
geometry and some acquaintance with modern analysis, the book
is reasonably self-contained. The book succeeds very well in
laying out the foundations of modern Riemannian geometry and
geometric analysis. It introduces a number of key techniques
and provides a representative overview of the
field.”
“For readers familiar with the basics of differential
geometry and some acquaintance with modern analysis, the book
is reasonably self-contained. The book succeeds very well in
laying out the foundations of modern Riemannian geometry and
geometric analysis. It introduces a number of key techniques
and provides a representative overview of the
field.”Monatshefte für Mathematik
Monatshefte für Mathematik
