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Hardcover ISBN:  9781470473020 
Product Code:  GSM/236 
List Price:  $135.00 
MAA Member Price:  $121.50 
AMS Member Price:  $108.00 
Softcover ISBN:  9781470475369 
Product Code:  GSM/236.S 
List Price:  $89.00 
MAA Member Price:  $80.10 
AMS Member Price:  $71.20 
eBook ISBN:  9781470475352 
Product Code:  GSM/236.E 
List Price:  $85.00 
MAA Member Price:  $76.50 
AMS Member Price:  $68.00 
Softcover ISBN:  9781470475369 
eBook ISBN:  9781470475352 
Product Code:  GSM/236.S.B 
List Price:  $174.00 $131.50 
MAA Member Price:  $156.60 $118.35 
AMS Member Price:  $139.20 $105.20 

Book DetailsGraduate Studies in MathematicsVolume: 236; 2024; 282 ppMSC: Primary 53; 30
Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and curvature bounded below (CBB). Even though the definitions of the two classes of spaces are similar, their properties and known applications are quite different.
The goal of this book is to give a comprehensive exposition of the structure theory of Alexandrov spaces with curvature bounded above and below. It includes all the basic material as well as selected topics inspired by considering Alexandrov spaces with CBA and with CBB simultaneously. The book also includes an extensive problem list with solutions indicated for every problem.
ReadershipGraduate students and researchers interested in geometry.

Table of Contents

Preliminaries

Model plane

Metric spaces

Maps and functions

Ultralimits

Space of spaces

The ghost of Euclid

Dimension theory

Fundamentals

Fundamentals of curvature bounded below

Fundamentals of curvature bounded above

Kirszbraun revisited

Warped products

Polyhedral spaces

Structure and tools

First order differentiation

Dimension of CAT spaces

Dimension of CBB spaces

Gradient flow

Appendix A. Semisolutions


Additional Material

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Alexandrov spaces are defined via axioms similar to those of the Euclid axioms but where certain equalities are replaced with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above (CBA) and curvature bounded below (CBB). Even though the definitions of the two classes of spaces are similar, their properties and known applications are quite different.
The goal of this book is to give a comprehensive exposition of the structure theory of Alexandrov spaces with curvature bounded above and below. It includes all the basic material as well as selected topics inspired by considering Alexandrov spaces with CBA and with CBB simultaneously. The book also includes an extensive problem list with solutions indicated for every problem.
Graduate students and researchers interested in geometry.

Preliminaries

Model plane

Metric spaces

Maps and functions

Ultralimits

Space of spaces

The ghost of Euclid

Dimension theory

Fundamentals

Fundamentals of curvature bounded below

Fundamentals of curvature bounded above

Kirszbraun revisited

Warped products

Polyhedral spaces

Structure and tools

First order differentiation

Dimension of CAT spaces

Dimension of CBB spaces

Gradient flow

Appendix A. Semisolutions