Alexandrov Geometry: Foundations

Alexandrov Geometry: Foundations

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Alexandrov spaces are defined via axioms similar to those given by Euclid. The Alexandrov axioms replace certain equalities with inequalities. Depending on the signs of the inequalities, we obtain Alexandrov spaces with curvature bounded above and curvature bounded below. The definitions of the two classes of spaces are similar, but their properties and known applications are quite different. Our approach is novel in its attention to the interrelatedness of the two fields, and its emphasis on the way each illuminates the other.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 the two contexts simultaneously. We only consider the intrinsic theory, leaving applications aside. This book includes material up to the definition of dimension. Another volume still in preparation will cover further topics.
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Data sheet

Name of the Author
Alexander
Anton
Kapovitch
STEPHANIE
Vitali and Petrunin
Language
English
Series
Graduate Studies in Mathematics
Release date
2023
Volume
236

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Alexandrov Geometry: Foundations

Alexandrov spaces are defined via axioms similar to those given by Euclid. The Alexandrov axioms replace certain equalities with inequalities. Depending on t...

Write your review

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