Author | Tromba, Anthony J. author |
---|---|
Title | Teichmรผller Theory in Riemannian Geometry [electronic resource] / by Anthony J. Tromba |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1992 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8613-0 |
Descript | IV, 220 p. online resource |
0 Mathematical Preliminaries -- 1 The Manifolds of Teichmรผller 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 Poincarรฉโs Theorem -- 1.6 The Manifold Ms-1 and the Diffeomorphism with Ms / s -- 2 The Construction of Teichmรผller 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 Teichmรผller Space -- 2.5 The Principal Bundles of Teichmรผller Theory -- 2.6 The Weil-Petersson Metric on T(M) -- 3 T(M) is a Cell -- 3.1 Dirichletโs Energy on Teichmรผller Space -- 3.2 The Properness of Dirichletโs Energy -- 3.3 Teichmรผller Space is a Cell -- 3.4 Topological Implications; The Contractibility of D0 -- 4 The Complex Structure on Teichmรผller 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 Kรคhler -- 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 Teichmรผller Space with Respect to its Weil-Petersson Metric -- 5.5 An Asymptotic Property of Weil-Petersson Geodesies -- 6 The Pluri-Subharmonicity of Dirichletโs Energy on T(M); T(M) is a Stein-Manifold -- 6.1 Pluri-Subharmonic Functions and Complex Manifolds -- 6.2 Dirichletโs Energy is Strictly Pluri-Subharmonic -- 6.3 Wolfโs Form of Dirichletโs Energy on T(M) is Strictly Weil-Petersson Convex -- 6.4 The Nielsen Realization Problem -- A Proof of Lichnerowiczโ Formula -- B On Harmonic Maps -- C The Mumford Compactness Theorem -- D Proof of the Collar Lemma -- E The Levi-Form of Dirichletโs Energy -- F Riemann-Roch and the Dimension of Teichmรผller Space -- Indexes -- Index of Notation -- A Chart of the Maps Used -- Index of Key Words