Abstract
By a length-preserving flow, we provide a new proof of a conjecture on the reverse isoperimetric inequality composed by Pan et al. (Math Inequal Appl 13:329–338, 2010), which states that if \(\gamma \) is a convex curve with length L and enclosed area A, then the best constant \(\varepsilon \) in the inequality
is \(\pi \), where \({\tilde{A}}\) denotes the oriented area of the locus of its curvature centers.
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This work was supported by the Fundamental Research Funds for the Central Universities (Nos. 3132020172, 3132019177).
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Yang, Y., Wu, W. The reverse isoperimetric inequality for convex plane curves through a length-preserving flow. Arch. Math. 116, 107–113 (2021). https://doi.org/10.1007/s00013-020-01541-5
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DOI: https://doi.org/10.1007/s00013-020-01541-5