Juha Heinonen (1960-2007) was Professor of Mathematics at the University of Michigan. His principal areas of research interest included quasiconformal mappings, nonlinear potential theory, and analysis on metric spaces. He was the author of over 60 research articles, including several posthumously, and two textbooks. A member of the Finnish Academy of Science and Letters, Heinonen received the Excellence in Research Award from the University of Michigan in 1997 and gave an invited lecture at the International Congress of Mathematicians in Beijing in 2002.
Inhaltsangabe
Preface 1. Introduction 2. Review of basic functional analysis 3. Lebesgue theory of Banach space-valued functions 4. Lipschitz functions and embeddings 5. Path integrals and modulus 6. Upper gradients 7. Sobolev spaces 8. Poincaré inequalities 9. Consequences of Poincaré inequalities 10. Other definitions of Sobolev-type spaces 11. Gromov-Hausdorff convergence and Poincaré inequalities 12. Self-improvement of Poincaré inequalities 13. An Introduction to Cheeger's differentiation theory 14. Examples, applications and further research directions References Notation index Subject index.
Preface 1. Introduction 2. Review of basic functional analysis 3. Lebesgue theory of Banach space-valued functions 4. Lipschitz functions and embeddings 5. Path integrals and modulus 6. Upper gradients 7. Sobolev spaces 8. Poincaré inequalities 9. Consequences of Poincaré inequalities 10. Other definitions of Sobolev-type spaces 11. Gromov-Hausdorff convergence and Poincaré inequalities 12. Self-improvement of Poincaré inequalities 13. An Introduction to Cheeger's differentiation theory 14. Examples, applications and further research directions References Notation index Subject index.
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