Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures : Lecture Notes in Mathematics - Lutz Habermann

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Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures

By: Lutz Habermann, L. Habermann

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Paperback | 1 October 2000

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136 Pages

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This monograph deals with recent questions of conformal geometry. It provides in detail an approach to studying moduli spaces of conformal structures, using a new canonical metric for conformal structures. This book is accessible to readers with basic knowledge in differential geometry and global analysis. It addresses graduates and researchers.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Functional Analysis & Transforms Geometry Differential & Riemannian Geometry Algebraic Geometry Medicine Medicine in General Numerical Analysis

Preliminaries	p. 1
Geometric preliminaries	p. 1
Analytic preliminaries	p. 6
A canonical metric for flat conformal manifolds	p. 11
Motivation of the approach	p. 12
The conformal Laplacian	p. 16
Definition and basic properties	p. 22
The metrics of Apanasov-Kulkarni-Pinkall and Nayatani	p. 25
Kleinian groups and moduli spaces	p. 33
Description of the canonical metric by Kleinian groups	p. 33
Moduli spaces of flat conformal structures	p. 38
The geometry of B[subscript o][superscript +] (S[superscript 1] x S[superscript 2])	p. 45
Asymptotics: The flat case	p. 55
Degenerating flat conformal structures	p. 55
The behavior near scalar flat structures	p. 70
Consequences for the geometry of B[subscript o][superscript +] (M)	p. 74
Generalization in low dimensions	p. 83
The canonical metric as metric of constant mass	p. 83
The canonical metric: The general case	p. 88
The regularity of the canonical metric	p. 97
The moduli space of all conformal structures	p. 101
The generalized metric near scalar flat structures	p. 101
Infinite distance components of the boundary	p. 105
References	p. 109
Index	p. 115
Table of Contents provided by Blackwell. All Rights Reserved.

Riemannian Metrics of Constant Mass and Moduli Spaces of Conformal Structures

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