Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON SOME GEOMETRIC INEQUALITIES ON ℓ-CONVEX LEGENDRE CURVES

  • Hongxin Guo (Department of mathematics Wenzhou University) ;
  • Jiehao Xia (Department of mathematics Wenzhou University)
  • Received : 2025.07.31
  • Accepted : 2025.12.02
  • Published : 2026.07.31
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Abstract

In this paper we study ℓ-convex Legendre curve which is a proper generalization of regular strictly convex curve. We prove several new geometric inequalities for ℓ-convex Legendre curves. Our results generalize two recent results which were proven by Kwong-Lee on the higher order Wirtinger inequalities for regular curves and by Li-Wang on geometric inequalities for Legendre curves.

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Acknowledgement

This work was financially supported by Zhejiang Provincial Natural Science Foundation of China under grant no. LY22A010007.