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Boundary behaviour of the span metric and its higher-order curvatures

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Abstract

In this note, we use scaling principle to study the boundary behaviour of the span metric and its higher-order curvatures on finitely connected Jordan planar domains. A localization of this metric near boundary points of finitely connected Jordan domains is also obtained. Further, we obtain boundary sharp estimates for the span metric near \( C^2 \)-smooth boundary points on such domains.

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Acknowledgements

The author would like to thank Kaushal Verma for fruitful discussions. The author also would like to thank the referee for carefully reading the paper, and for many useful suggestions that have improved the paper.

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  1. Indian Institute of Science Education and Research Kolkata, Mohanpur, India

    Amar Deep Sarkar

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  1. Amar Deep Sarkar
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The author is supported by the postdoctoral fellowship of Harish-Chandra Research Institute, Allahabad.

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Sarkar, A.D. Boundary behaviour of the span metric and its higher-order curvatures. Complex Anal Synerg 8, 16 (2022). https://doi.org/10.1007/s40627-022-00106-2

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