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arXiv · 2512.05233

Ratio of Intrinsic Metric to Extrinsic Metric and Volume

Berk Ceylan
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Abstract

We study the relationship between the ratio of intrinsic to extrinsic metrics and area. For certain surfaces inside unit ball in R3 we give lower bound on the maximum of ratio in terms of its area. We also give examples to show non-existence of global lower bounds.

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Berk Ceylan. 2025-12-04. Ratio of Intrinsic Metric to Extrinsic Metric and Volume. https://arxiv.org/abs/2512.05233

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