Stability and construction of negatively curved Einstein metrics
Stability and construction of negatively curved Einstein metrics
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DissertationPrüfungsdatum
11.07.2025Datum der Veröffentlichung
23.07.2025Erstgutachter
Hamenstädt, UrsulaZweitgutachter
Hein, Hans-JoachimMetadaten
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Inhalt
We prove several stability results for negatively curved Einstein metrics. The main applications of these results are:
(1) The construction of infinitely many non-trivial closed Einstein manifolds with negative sectional curvature in every dimension at least four. In dimensions at least, five these are the first non-trivial examples of such manifolds.
(2) A Ricci flow free proof of Perelman's hyperbolization theorem for topologically complicated 3-manifolds. Moreover, the volume of the hyperbolic metric is bounded from below by a number measuring the topological complexity of the underlying closed 3-manifold.
(1) The construction of infinitely many non-trivial closed Einstein manifolds with negative sectional curvature in every dimension at least four. In dimensions at least, five these are the first non-trivial examples of such manifolds.
(2) A Ricci flow free proof of Perelman's hyperbolization theorem for topologically complicated 3-manifolds. Moreover, the volume of the hyperbolic metric is bounded from below by a number measuring the topological complexity of the underlying closed 3-manifold.
Klassifikation (DDC)
510 MathematikJäckel, Frieder: Stability and construction of negatively curved Einstein metrics. - Bonn, 2025. - Dissertation, Rheinische Friedrich-Wilhelms-Universität Bonn.
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-84055
Online-Ausgabe in bonndoc: https://nbn-resolving.org/urn:nbn:de:hbz:5-84055
@phdthesis{handle:20.500.11811/13264,
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-84055,
author = {{Frieder Jäckel}},
title = {Stability and construction of negatively curved Einstein metrics},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2025,
month = jul,
note = {We prove several stability results for negatively curved Einstein metrics. The main applications of these results are:
(1) The construction of infinitely many non-trivial closed Einstein manifolds with negative sectional curvature in every dimension at least four. In dimensions at least, five these are the first non-trivial examples of such manifolds.
(2) A Ricci flow free proof of Perelman's hyperbolization theorem for topologically complicated 3-manifolds. Moreover, the volume of the hyperbolic metric is bounded from below by a number measuring the topological complexity of the underlying closed 3-manifold.},
url = {https://hdl.handle.net/20.500.11811/13264}
}
urn: https://nbn-resolving.org/urn:nbn:de:hbz:5-84055,
author = {{Frieder Jäckel}},
title = {Stability and construction of negatively curved Einstein metrics},
school = {Rheinische Friedrich-Wilhelms-Universität Bonn},
year = 2025,
month = jul,
note = {We prove several stability results for negatively curved Einstein metrics. The main applications of these results are:
(1) The construction of infinitely many non-trivial closed Einstein manifolds with negative sectional curvature in every dimension at least four. In dimensions at least, five these are the first non-trivial examples of such manifolds.
(2) A Ricci flow free proof of Perelman's hyperbolization theorem for topologically complicated 3-manifolds. Moreover, the volume of the hyperbolic metric is bounded from below by a number measuring the topological complexity of the underlying closed 3-manifold.},
url = {https://hdl.handle.net/20.500.11811/13264}
}
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