A generalization of Riemann mappings and geometric structures on a space of domains in C^n / [electronic resource] Stephen Semmes.

"July 1991, volume 98, number 472 (third of 4 numbers)."

Includes bibliographical references (p. 97-98).

1. Introduction 2. Riemann mappings, Green's functions, and extremal disks 3. Uniqueness of Riemann mappings, and Riemann mappings onto circled domains 4. Riemann mappings and the Kobayashi indicatrix 5. Existence of Riemann mappings whose image is a given smooth, strongly convex domain 6. Riemann mappings and HCMA, part 1 7. Riemann mappings and HCMA, part 2 8. Riemann mappings and liftings to $\mathcal {C}$ 9. Spaces of Riemann mappings, spaces of domains 10. Spaces of Riemann mappings as complex varieties 11. Homogeneous mappings, completely circled domains, and the Kobayashi indicatrix 12. A natural action on $\hat {\mathcal {R}}$ 13. The action of $\mathcal {H}$ on domains in $\mathbf {C}^n$ 14. Riemannian geometry on $\mathcal {D}^\infty $; preliminary discussion 15. Some basic facts and definitions concerning the metric on $\mathcal {D}^\infty _{co}$ 16. The metric on $\mathcal {D}^\infty _{co}$, circled domains, and the Kobayashi indicatrix 17. The Riemannian metric and the action of $\mathcal {H}$ 18. The first variation of the energy of a curve in $\mathcal {D}^\infty _{co}$ 19. Geometry on $\mathcal {R}^\infty $ 20. Another approach to Riemannian geometry on $\mathcal {R}^\infty $ 21. A few remarks about the Hermitian geometry on $\hat {\mathcal {R}}^\infty $

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Electronic reproduction. Providence, Rhode Island : American Mathematical Society. 2012

Mode of access : World Wide Web

Description based on print version record.