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arXiv · 2605.26780

A family of parametric isoperimetric-type inequalities with multiple geometric quantities

Heran Zhao
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Abstract

We establish a family of parametric isoperimetric-type inequalities with multiple geometric quantities for closed convex curves. These inequalities hold under certain parameter conditions. We also prove the equality conditions. Some new inequalities and improved versions of proven inequalities are derived by adjusting the parameters. Such inequalities are stable under stronger conditions.

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Heran Zhao. 2026-05-26. A family of parametric isoperimetric-type inequalities with multiple geometric quantities. https://arxiv.org/abs/2605.26780

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