Teichmüller Theory in Riemannian Geometry
Abstract
0 Mathematical Preliminaries.- 1 The Manifolds of Teichmuller Theory.- 1.1 The Manifolds A and As.- 1.2 The Riemannian Manifolds M and Ms.- 1.3 The Diffeomorphism Ms /? s ? As.- 1.4 Some Differential Operators and their Adjoints.- 1.5 Proof of Poincare's Theorem.- 1.6 The Manifold Ms-1 and the Diffeomorphism with Ms / s.- 2 The Construction of Teichmuller Space.- 2.1 A Rapid Course in Geodesic Theory.- 2.2 The Free Action of D0 on M-1.- 2.3 The Proper Action of D0 on M-1.- 2.4 The Construction of Teichmuller Space.- 2.5 The Principal Bundles of Teichmuller Theory.- 2.6 The Weil-Petersson Metric on T(M).- 3 T(M) is a Cell.- 3.1 Dirichlet's Energy on Teichmuller Space.- 3.2 The Properness of Dirichlet's Energy.- 3.3 Teichmuller Space is a Cell.- 3.4 Topological Implications The Contractibility of D0.- 4 The Complex Structure on Teichmuller Space.- 4.1 Almost Complex Principal Fibre Bundles.- 4.2 Abresch-Fischer Holomorphic Coordinates for A.- 4.3 Abresch-Fischer Holomorphic Coordinates for T(M).- 5 Properties of the Weil-Petersson Metric.- 5.1 The Weil-Petersson Metric is Kahler.- 5.2 The Natural Algebraic Connection on A.- 5.3 Further Properties of the Algebraic Connection and the non-Integrability of the Horizontal Distribution on A.- 5.4 The Curvature of Teichmuller Space with Respect to its Weil-Petersson Metric.- 5.5 An Asymptotic Property of Weil-Petersson Geodesies.- 6 The Pluri-Subharmonicity of Dirichlet's Energy on T(M) T(M) is a Stein-Manifold.- 6.1 Pluri-Subharmonic…
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Teichmüller space T(Σ) is a C∞ manifold of dimension 6genus(Σ)-6 diffeomorphic to R^{6genus(Σ)-6}.
“T (Σ) is a C ∞ manifold of dimension dim T (Σ) = 6genus(Σ) -6 diffeomorphic to R 6genus(Σ) -6”
From On the global evolution problem in 2 + 1 gravity (1997) · cites this paper as [5]
Teichmüller space T(Σ) is geodesically convex with respect to the Weil-Peterson metric but not complete.
“T (Σ) is geodesically convex w.r.t. the Weil-Peterson metric but not complete.”
From On the global evolution problem in 2 + 1 gravity (1997) · cites this paper as [5]
The Dirichlet energy ̃E is a proper function on Teichmüller space T(Σ).
“Proposition 2.2 ([5]) . 1. The Dirichlet energy ˜ E is a proper function on T (Σ) .”
From On the global evolution problem in 2 + 1 gravity (1997) · cites this paper as [5]
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On the global evolution problem in 2 + 1 gravity
Anderson, L., Moncrief, V., & Tromba, A. J. (1997) · Journal of Geometry and Physics · doi:10.1016/s0393-0440(97)87804-7 · Cited by 72 · see citing works
Self-citation
- Authors
- Tromba, A. J.
- Affiliations
- University of California, Santa Cruz (US)
- Corresponding author
- Tromba, Anthony J.
- Venue
- Birkhäuser Basel eBooks
- Publisher
- Birkhäuser Basel
- Published
- 1992
- OpenAlex
- W1759497388
- Cited by
- 169
- References
- 0
- Citations by year
- 2026: 5 · 2025: 7 · 2024: 4 · 2023: 5 · 2022: 5 · 2021: 14 · 2020: 7 · 2019: 17 · 2018: 7 · 2017: 9 · 2016: 11 · 2015: 1 · 2014: 7 · 2013: 8 · 2012: 8
- FWCI
- 1.85
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Birkhäuser Basel eBooks (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Geometry and Topology › Geometric and Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Geometry and complex manifolds
- Physical Sciences › Mathematics › Applied Mathematics › Geometric Analysis and Curvature Flows
- Keywords
- Teichmüller space, Weil-Petersson metric, Riemannian geometry, Dirichlet energy, Stein manifolds, principal bundles, Poincaré's theorem, moduli space of Riemann surfaces, holomorphic sectional curvature
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