scholarly journals Special Kähler structures, cubic differentials and hyperbolic metrics

2020 ◽  
Vol 26 (3) ◽  
Author(s):  
Andriy Haydys ◽  
Bin Xu
Keyword(s):  
Hyperbolic Metrics ◽  
Kähler Structures

scholarly journals Correction to: Special Kähler structures, cubic differentials and hyperbolic metrics

2021 ◽  
Vol 27 (2) ◽  
Author(s):  
Andriy Haydys ◽  
Bin Xu
Keyword(s):  
Hyperbolic Metrics ◽  
Kähler Structures

A correction to this paper has been published: https://doi.org/10.1007/s00029-021-00643-4

scholarly journals Deformation classes in generalized Kähler geometry

2020 ◽  
Vol 7 (1) ◽  
pp. 241-256
Author(s):  
Matthew Gibson ◽  
Jeffrey Streets
Keyword(s):  
Symmetry Group ◽  
Ricci Flow ◽  
Kahler Geometry ◽  
Poisson Tensor ◽  
Natural Extensions ◽  
Generalized Kähler Geometry ◽  
Kähler Structures

AbstractWe describe natural deformation classes of generalized Kähler structures using the Courant symmetry group, which determine natural extensions of the notions of Kähler class and Kähler cone to generalized Kähler geometry. We show that the generalized Kähler-Ricci flow preserves this generalized Kähler cone, and the underlying real Poisson tensor.

scholarly journals Kähler structures on compact solvmanifolds

1990 ◽  
Vol 108 (4) ◽  
pp. 971-971
Author(s):  
Chal Benson ◽  
Carolyn S. Gordon
Keyword(s):  
Kähler Structures

scholarly journals Topological flows for hyperbolic groups

2020 ◽  
pp. 1-47
Author(s):  
RYOKICHI TANAKA
Keyword(s):  
Hausdorff Dimension ◽  
Radon Measure ◽  
Hyperbolic Group ◽  
Hyperbolic Metric ◽  
Hyperbolic Groups ◽  
Group Invariant ◽  
Hyperbolic Metrics ◽  
Measure Class

Abstract Weshow that for every non-elementary hyperbolic group the Bowen–Margulis current associated with a strongly hyperbolic metric forms a unique group-invariant Radon measure class of maximal Hausdorff dimension on the boundary square. Applications include a characterization of roughly similar hyperbolic metrics via mean distortion.

scholarly journals Boundary Behaviour of Weil–Petersson and Fibre Metrics for Riemann Moduli Spaces

2017 ◽  
Vol 2019 (16) ◽  
pp. 5012-5065 ◽  
Author(s):  
Richard Melrose ◽  
Xuwen Zhu
Keyword(s):  
Moduli Spaces ◽  
Asymptotic Expansions ◽  
Conformal Factor ◽  
Complex Structures ◽  
Stable Range ◽  
Universal Curve ◽  
Boundary Behaviour ◽  
Hyperbolic Metrics ◽  
Push Forward ◽  
Complete Metrics

Abstract The Weil–Petersson and Takhtajan–Zograf metrics on the Riemann moduli spaces of complex structures for an $n$-fold punctured oriented surface of genus $g,$ in the stable range $g+2n>2,$ are shown here to have complete asymptotic expansions in terms of Fenchel–Nielsen coordinates at the exceptional divisors of the Knudsen–Deligne–Mumford compactification. This is accomplished by finding a full expansion for the hyperbolic metrics on the fibres of the universal curve as they approach the complete metrics on the nodal curves above the exceptional divisors and then using a push-forward theorem for conormal densities. This refines a two-term expansion due to Obitsu–Wolpert for the conformal factor relative to the model plumbing metric which in turn refined the bound obtained by Masur. A similar expansion for the Ricci metric is also obtained.

scholarly journals Conformal Compactification of Asymptotically Locally Hyperbolic Metrics

2010 ◽  
Vol 21 (4) ◽  
pp. 1085-1118 ◽  
Author(s):  
Eric Bahuaud ◽  
Romain Gicquaud
Keyword(s):  
Hyperbolic Metrics
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