The Metric Induced by the Robin Function is popular PDF and ePub book, written by Norman Levenberg in 1991, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Metric Induced by the Robin Function can be Read Online from any device for your convenience.
The Metric Induced by the Robin Function Book PDF Summary
This paper continues Yamaguchi's earlier work on the Robin function for bounded domains in [bold]C[italic superscript]n. Yamaguchi showed that if the domain [italic]D is smoothly bounded and pseudoconvex, then the Robin function and its logarithm are both real analytic strongly pseudoconvex exhaustions of the domain. It follows that they may be used as potentials to define Kähler metrics on the domain. In this paper, the authors study the properties of these Kähler metrics, concentrating on the question of completeness. By using an affine scaling technique to blow up the domain at points near the boundary (the scaling constant grows roughly as the inverse of the distance to the boundary), the authors study in some detail the behaviour of the Robin function and the induced metric near the boundary of the domain. They show that if the domain is either strongly pseudoconvex or geometrically convex, then the metric associated to the logarithm of the Robin function is complete. They also conjecture that this is true in general for any smoothly bounded pseudoconvex domain.
Detail Book of The Metric Induced by the Robin Function PDF
- Author : Norman Levenberg
- Release : 30 September 1991
- Publisher : American Mathematical Soc.
- ISBN : 9780821825204
- Genre : Mathematics
- Total Page : 169 pages
- Language : English
- PDF File Size : 14,5 Mb
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