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Robin Functions for Complex Manifolds and Applications
Kang-Tae Kim, Pohang University of Science and Technology, South Korea, Norman Levenberg, Indiana University, Bloomington, IN, and Hiroshi Yamaguchi, Shiga University, Japan
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Memoirs of the American Mathematical Society
2011; 111 pp; softcover
Volume: 209
ISBN-10: 0-8218-4965-4
ISBN-13: 978-0-8218-4965-1
List Price: US$70
Individual Members: US$42
Institutional Members: US$56
Order Code: MEMO/209/984
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In a previous Memoirs (Vol. 92, No. 448), Levenberg and Yamaguchi analyzed the second variation of the Robin function \(-\lambda(t)\) associated to a smooth variation of domains in \(\mathbb{C}^n\) for \(n\geq 2\). In the current work, the authors study a generalization of this second variation formula to complex manifolds \(M\) equipped with a Hermitian metric \(ds^2\) and a smooth, nonnegative function \(c\).

Table of Contents

  • Introduction
  • The variation formula
  • Subharmonicity of \(-\lambda\)
  • Rigidity
  • Complex Lie groups
  • Complex homogeneous spaces
  • Flag space
  • Appendix A
  • Appendix B
  • Appendix C
  • Bibliography
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