Alexandrov Geometry: Foundations
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 de...
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| Hauptverfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2024]
|
| Schriftenreihe: | Graduate Studies in Mathematics Series
Volume 236 |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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. |
| Beschreibung: | Description based on publisher supplied metadata and other sources |
| Beschreibung: | 1 Online-Ressource (xvii, 282 Seiten) Illustrationen |
| ISBN: | 9781470475352 9781470473020 |
| DOI: | 10.1090/gsm/236 |
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| 520 | 3 | |a 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. | |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Mathematik |
| doi_str_mv | 10.1090/gsm/236 |
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| indexdate | 2025-03-20T19:09:29Z |
| institution | BVB |
| isbn | 9781470475352 9781470473020 |
| language | English |
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| spelling | Alexander, Stephanie 1941- (DE-588)1187370002 aut Alexandrov Geometry Foundations Providence, Rhode Island American Mathematical Society [2024] © 2024 1 Online-Ressource (xvii, 282 Seiten) Illustrationen txt rdacontent c rdamedia cr rdacarrier Graduate Studies in Mathematics Series Volume 236 Description based on publisher supplied metadata and other sources 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. Kapovitch, Vitali 1969- (DE-588)1157920950 aut Petrunin, Anton 1968- (DE-588)1191109208 aut Erscheint auch als Druck-Ausgabe 978-1-4704-7302-0 Graduate Studies in Mathematics Series Volume 236 (DE-604)BV044714883 236 https://doi.org/10.1090/gsm/236 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Alexander, Stephanie 1941- Kapovitch, Vitali 1969- Petrunin, Anton 1968- Alexandrov Geometry Foundations Graduate Studies in Mathematics Series |
| title | Alexandrov Geometry Foundations |
| title_auth | Alexandrov Geometry Foundations |
| title_exact_search | Alexandrov Geometry Foundations |
| title_full | Alexandrov Geometry Foundations |
| title_fullStr | Alexandrov Geometry Foundations |
| title_full_unstemmed | Alexandrov Geometry Foundations |
| title_short | Alexandrov Geometry |
| title_sort | alexandrov geometry foundations |
| title_sub | Foundations |
| url | https://doi.org/10.1090/gsm/236 |
| volume_link | (DE-604)BV044714883 |
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