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The metric induced by the Robin function

About this Title

Norman Levenberg and Hiroshi Yamaguchi

Publication: Memoirs of the American Mathematical Society
Publication Year 1991: Volume 92, Number 448
ISBNs: 978-0-8218-2520-4 (print); 978-1-4704-0874-9 (online)
MathSciNet review: 1061928
MSC: Primary 32F15; Secondary 31B25

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Table of Contents


  • 1. Levi-curvature
  • 2. Smooth variation of domains
  • 3. Boundary behavior of the Robin function $\Lambda (\xi )$
  • 4. Proof of Lemma 3.1
  • 5. Proof of Lemma 3.1, continued
  • 6. Limiting formulas
  • 7. Strict plurisubharmonicity of $-\Lambda (\xi )$, $\log (-\Lambda (\xi ))$
  • 8. The Robin function and the Bergman kernel
  • 9. Metric induced by Robin function
  • 10. Strictly pseudoconvex boundary points
  • 11. Explicit formulas for a half-space
  • 12. Sufficient conditions for completeness of the $\Lambda $-metric
  • 13. An example with $\ell _2(\xi , a) \not \geq c|\ell _1 (\xi , a)|^2$