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Jürgen Jost

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New Directions in Dirichlet Forms

Editors: J. Jost, W. Kendall, U. Mosco, M. Röckner, K.-T. Sturm
International Press/AMS, 1998

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Table of Contents

Jürgen Jost: Nonlinear Dirichlet Forms

1.1 Introduction
1.2 Definition and properties of generalized Dirichlet forms
1.3 Resolvents, semigroups, and variational aspects
1.4 Convergence properties
1.5 Generalized harmonic maps
1.6 Appendix: Geometric notions

Wilfrid S. Kendall: From Stochastic Parallel Transport to Harmonic Maps

2.1 Introduction
2.2 Stochastic differential geometry
2.3 Distance and semimartingales
2.4 Coupling and parallel transport
2.5 Harmonic map Dirichlet problem

Umberto Mosco: Dirichlet forms and self-similarity

3.1 Introduction
3.2 Self-similar fractals
3.3 Variational fractals
3.4 The Lagrangian metrics
3.5 The intrinsic homogeneous structure
3.6 Field operators and spectral asymptotics
3.7 Local solutions
3.8 Scaled Poincaré inequalities
3.9 Nash inequalities and Morrey-Sobolev imbeddings

Michael Röckner: Stochastic analysis on configuration spaces: basic ideas and recent results

4.1 Introduction
4.2 Lifting the geometry from the base manifold to the configuration space
4.3 Infinite dimensional analysis and Brownian motion on configuration spaces
4.4 Classical Dirichlet forms on configuration spaces w.r.t. general measures
4.5 Intrinsic metric on configuration spaces
4.6 Gibbs measures on configuration spaces
4.7 Integration by parts characterization of canonical Gibbs measures
4.8 Infinite interacting particle systems
4.9 Ergodicity

Karl-Theodor Sturm: The Geometric Aspect of Dirichlet Forms

5.1 Introduction
5.2 Estimates for Semigroups and Resolvents
5.3 Capacity Estimates and Applications
5.4 The Intrinsic Metric
5.5 Examples

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