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Alexandrov Geometry: Foundations
 
Stephanie Alexander University of Illinois, Urbana-Champaign, Urbana, IL
Vitali Kapovitch University of Toronto, Toronto, ON, Canada
Anton Petrunin Pennsylvania State University, College State, PA
Hardcover ISBN:  978-1-4704-7302-0
Product Code:  GSM/236
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
Softcover ISBN:  978-1-4704-7536-9
Product Code:  GSM/236.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
eBook ISBN:  978-1-4704-7535-2
Product Code:  GSM/236.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
Softcover ISBN:  978-1-4704-7536-9
eBook: ISBN:  978-1-4704-7535-2
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
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
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Alexandrov Geometry: Foundations
Stephanie Alexander University of Illinois, Urbana-Champaign, Urbana, IL
Vitali Kapovitch University of Toronto, Toronto, ON, Canada
Anton Petrunin Pennsylvania State University, College State, PA
Hardcover ISBN:  978-1-4704-7302-0
Product Code:  GSM/236
List Price: $135.00
MAA Member Price: $121.50
AMS Member Price: $108.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
Softcover ISBN:  978-1-4704-7536-9
Product Code:  GSM/236.S
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
eBook ISBN:  978-1-4704-7535-2
Product Code:  GSM/236.E
List Price: $85.00
MAA Member Price: $76.50
AMS Member Price: $68.00
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
Softcover ISBN:  978-1-4704-7536-9
eBook ISBN:  978-1-4704-7535-2
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
Not yet published - Preorder Now!
Expected availability date: June 30, 2024
  • Book Details
     
     
    Graduate Studies in Mathematics
    Volume: 2362024; 282 pp
    MSC: 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.

    Readership

    Graduate 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
    • Semisolutions
    • Bibliography
    • Index
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 2362024; 282 pp
MSC: 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.

Readership

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
  • Semisolutions
  • Bibliography
  • Index
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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