A Note on variation of bergman metrics on riemann surfaces under pseudoconvexity

Abstract

We study the variation of the Bergman disk δ_ϵ(t) with center ζ(t) and radius ϵ>0 on the moving Riemann surface R(t) with parameter t in a disk B, and show that, if the total space

is a strictly pseudoconvex domain, then, for sufficiently small ϵ > 0, the domain

is also pseudoconvex in case ζ(t) is holomorphic on B.

Keywords:

• Riemann surface
• Bergman metric
• Pseudoconvexity
• AMS Subject Classifications: 30C85
• 30F15
• 32F05
• 32H10

Acknowledgements

We thank Professors K.-T. Kim and F. Maitani for their comments to the proofs of Theorem 1 and Theorem 2, respectively.

Notes

e-mail: [email protected]

This article is dedicated to the late Professor Matts Essen of Uppsala University.

This article is dedicated to the late Professor Matts Essen of Uppsala University.

Additional information

Notes on contributors

Hiroshi Yamaguchi †

e-mail: [email protected] This article is dedicated to the late Professor Matts Essen of Uppsala University.