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Register a new userAn analogue of the squeezing function for projective maps
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In the spirit of Kobayashis applications of methods of invariant metrics to questions of projective geometry, we introduce a projective analogue of the complex squeezing function. Using Frankels work, we prove that for convex domains it stays uniformly bounded from below. In the case of strongly convex domains, we show that it tends to 1 at the boundary. This is applied to get a new proof of a projective analogue of the Wong-Rosay theorem.
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We describe the boundary behaviors of the squeezing functions for all bounded convex domains in $mathbb{C}^n$ and bounded domains with a $C^2$ strongly convex boundary point.
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In the present article, we define squeezing function corresponding to polydisk and study its properties. We investigate relationship between squeezing fuction and squeezing function corresponding to polydisk.
For a domain $D subset mathbb C^n$, the relationship between the squeezing function and the Fridman invariants is clarified. Furthermore, localization properties of these functions are obtained. As applications, some known results concerning their boundary behavior are extended.
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