Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / / G. Daniel Mostow.
Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini...
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Mostow, G. Daniel, author. aut http://id.loc.gov/vocabulary/relators/aut Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / G. Daniel Mostow. Princeton, NJ : Princeton University Press, [2016] ©1974 1 online resource (204 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 78 Frontmatter -- Contents -- §1. Introduction -- §2. Algebraic Preliminaries -- §3. The Geometry of χ : Preliminaries -- §4. A Metric Definition of the Maximal Boundary -- §5. Polar Parts -- §6. A Basic Inequality -- §7. Geometry of Neighboring Flats -- §8. Density Properties of Discrete Subgroups -- §8. Density Properties of Discrete Subgroups -- § 10. Pseudo Isometries of Simply Connected Spaces with Negative Curvature -- §11. Polar Regular Elements in Co-Compact Γ -- § 12. Pseudo-Isometric Invariance of Semi-Simple and Unipotent Elements -- §13. The Basic Approximation -- §14. The Map ∅̅ -- §15. The Boundary Map ∅0 -- §16. Tits Geometries -- §17. Rigidity for R-rank > 1 -- §18. The Restriction to Simple Groups -- §19. Spaces of R-rank 1 -- §20. The Boundary Semi-Metric -- §21. Quasi-Conformal Mappings Over K and Absolute Continuity on Almost All R-Circles -- §22. The Effect of Ergodicity -- §23. R-Rank 1 Rigidity Proof Concluded -- §24. Concluding Remarks -- Bibliography -- Backmatter restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Locally symmetric spaces are generalizations of spaces of constant curvature. In this book the author presents the proof of a remarkable phenomenon, which he calls "strong rigidity": this is a stronger form of the deformation rigidity that has been investigated by Selberg, Calabi-Vesentini, Weil, Borel, and Raghunathan.The proof combines the theory of semi-simple Lie groups, discrete subgroups, the geometry of E. Cartan's symmetric Riemannian spaces, elements of ergodic theory, and the fundamental theorem of projective geometry as applied to Tit's geometries. In his proof the author introduces two new notions having independent interest: one is "pseudo-isometries"; the other is a notion of a quasi-conformal mapping over the division algebra K (K equals real, complex, quaternion, or Cayley numbers). The author attempts to make the account accessible to readers with diverse backgrounds, and the book contains capsule descriptions of the various theories that enter the proof. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Lie groups. Riemannian manifolds. Rigidity (Geometry). Symmetric spaces. MATHEMATICS / Geometry / Differential. bisacsh Addition. Adjoint representation. Affine space. Approximation. Automorphism. Axiom. Big O notation. Boundary value problem. Cohomology. Compact Riemann surface. Compact space. Conjecture. Constant curvature. Corollary. Counterexample. Covering group. Covering space. Curvature. Diameter. Diffeomorphism. Differentiable function. Dimension. Direct product. Division algebra. Ergodicity. Erlangen program. Existence theorem. Exponential function. Finitely generated group. Fundamental domain. Fundamental group. Geometry. Half-space (geometry). Hausdorff distance. Hermitian matrix. Homeomorphism. Homomorphism. Hyperplane. Identity matrix. Inner automorphism. Isometry group. Jordan algebra. Matrix multiplication. Metric space. Morphism. Möbius transformation. Normal subgroup. Normalizing constant. Partially ordered set. Permutation. Projective space. Riemann surface. Riemannian geometry. Sectional curvature. Self-adjoint. Set function. Smoothness. Stereographic projection. Subgroup. Subset. Summation. Symmetric space. Tangent space. Tangent vector. Theorem. Topology. Tubular neighborhood. Two-dimensional space. Unit sphere. Vector group. Weyl group. Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 9783110442496 print 9780691081366 https://doi.org/10.1515/9781400881833 https://www.degruyter.com/isbn/9781400881833 Cover https://www.degruyter.com/document/cover/isbn/9781400881833/original |
language |
English |
format |
eBook |
author |
Mostow, G. Daniel, Mostow, G. Daniel, |
spellingShingle |
Mostow, G. Daniel, Mostow, G. Daniel, Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / Annals of Mathematics Studies ; Frontmatter -- Contents -- §1. Introduction -- §2. Algebraic Preliminaries -- §3. The Geometry of χ : Preliminaries -- §4. A Metric Definition of the Maximal Boundary -- §5. Polar Parts -- §6. A Basic Inequality -- §7. Geometry of Neighboring Flats -- §8. Density Properties of Discrete Subgroups -- § 10. Pseudo Isometries of Simply Connected Spaces with Negative Curvature -- §11. Polar Regular Elements in Co-Compact Γ -- § 12. Pseudo-Isometric Invariance of Semi-Simple and Unipotent Elements -- §13. The Basic Approximation -- §14. The Map ∅̅ -- §15. The Boundary Map ∅0 -- §16. Tits Geometries -- §17. Rigidity for R-rank > 1 -- §18. The Restriction to Simple Groups -- §19. Spaces of R-rank 1 -- §20. The Boundary Semi-Metric -- §21. Quasi-Conformal Mappings Over K and Absolute Continuity on Almost All R-Circles -- §22. The Effect of Ergodicity -- §23. R-Rank 1 Rigidity Proof Concluded -- §24. Concluding Remarks -- Bibliography -- Backmatter |
author_facet |
Mostow, G. Daniel, Mostow, G. Daniel, |
author_variant |
g d m gd gdm g d m gd gdm |
author_role |
VerfasserIn VerfasserIn |
author_sort |
Mostow, G. Daniel, |
title |
Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / |
title_full |
Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / G. Daniel Mostow. |
title_fullStr |
Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / G. Daniel Mostow. |
title_full_unstemmed |
Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / G. Daniel Mostow. |
title_auth |
Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / |
title_alt |
Frontmatter -- Contents -- §1. Introduction -- §2. Algebraic Preliminaries -- §3. The Geometry of χ : Preliminaries -- §4. A Metric Definition of the Maximal Boundary -- §5. Polar Parts -- §6. A Basic Inequality -- §7. Geometry of Neighboring Flats -- §8. Density Properties of Discrete Subgroups -- § 10. Pseudo Isometries of Simply Connected Spaces with Negative Curvature -- §11. Polar Regular Elements in Co-Compact Γ -- § 12. Pseudo-Isometric Invariance of Semi-Simple and Unipotent Elements -- §13. The Basic Approximation -- §14. The Map ∅̅ -- §15. The Boundary Map ∅0 -- §16. Tits Geometries -- §17. Rigidity for R-rank > 1 -- §18. The Restriction to Simple Groups -- §19. Spaces of R-rank 1 -- §20. The Boundary Semi-Metric -- §21. Quasi-Conformal Mappings Over K and Absolute Continuity on Almost All R-Circles -- §22. The Effect of Ergodicity -- §23. R-Rank 1 Rigidity Proof Concluded -- §24. Concluding Remarks -- Bibliography -- Backmatter |
title_new |
Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / |
title_sort |
strong rigidity of locally symmetric spaces. (am-78), volume 78 / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2016 |
physical |
1 online resource (204 p.) Issued also in print. |
contents |
Frontmatter -- Contents -- §1. Introduction -- §2. Algebraic Preliminaries -- §3. The Geometry of χ : Preliminaries -- §4. A Metric Definition of the Maximal Boundary -- §5. Polar Parts -- §6. A Basic Inequality -- §7. Geometry of Neighboring Flats -- §8. Density Properties of Discrete Subgroups -- § 10. Pseudo Isometries of Simply Connected Spaces with Negative Curvature -- §11. Polar Regular Elements in Co-Compact Γ -- § 12. Pseudo-Isometric Invariance of Semi-Simple and Unipotent Elements -- §13. The Basic Approximation -- §14. The Map ∅̅ -- §15. The Boundary Map ∅0 -- §16. Tits Geometries -- §17. Rigidity for R-rank > 1 -- §18. The Restriction to Simple Groups -- §19. Spaces of R-rank 1 -- §20. The Boundary Semi-Metric -- §21. Quasi-Conformal Mappings Over K and Absolute Continuity on Almost All R-Circles -- §22. The Effect of Ergodicity -- §23. R-Rank 1 Rigidity Proof Concluded -- §24. Concluding Remarks -- Bibliography -- Backmatter |
isbn |
9781400881833 9783110494914 9783110442496 9780691081366 |
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Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA649 |
callnumber-sort |
QA 3649 M78 |
url |
https://doi.org/10.1515/9781400881833 https://www.degruyter.com/isbn/9781400881833 https://www.degruyter.com/document/cover/isbn/9781400881833/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
516 - Geometry |
dewey-full |
516/.36 |
dewey-sort |
3516 236 |
dewey-raw |
516/.36 |
dewey-search |
516/.36 |
doi_str_mv |
10.1515/9781400881833 |
oclc_num |
979579084 |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Archive 1927-1999 |
is_hierarchy_title |
Strong Rigidity of Locally Symmetric Spaces. (AM-78), Volume 78 / |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 |
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