Geodesics for the capacity metric in doubly connected domains

Abstract

We give the qualitative behavior of geodesics of the capacity metric defined on the annulus and study the variation of its Gaussian curvature. We make explicit the relation between the capacities, the Bergman kernel and the reduced Bergman kernel on doubly connected domains and give some applications.

Keywords:

• Capacities
• Robin function
• Eisenstein series
• Bergman kernel
• Szegö kernel
• AMS 2000 Mathematics Subject Classifications: 11F11
• 30C40
• 30C85
• 31A15
• 32A25
• 34B30

Acknowledgements

The author expresses his sincere gratitude to Prof. A. Sebbar for his helpful discussions and encouragement throughout the work. The author is also indebted to Prof. B.Gustafsson for his kind help.

Notes

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Additional information

Notes on contributors

Nabil Aboudi *

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