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Anisotropic area-preserving flows for plane curves and entropy inequalities
Published online by Cambridge University Press: 23 September 2025
Abstract
This article describes two anisotropic area-preserving flows for plane curves, both of which are considered to deform one convex curve into another. Different monotonic entropy functions are identified under these flows, which can be utilized to derive two significant entropy inequalities: the log-Minkowski inequality and the curvature entropy inequality, as well as the Brunn–Minkowski inequality.
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society
Footnotes
Y.Y. is supported by the Educational Research Projects of China Transportation Education Research Association (Grant No. JT2024YB103), the Fundamental Research Funds for the Department of Education of Liaoning Province (Grant No. LJ212410151007), and the Fundamental Research Funds for the Central Universities (Grant No. 3132024198). Y.Z. is supported by the High-Level Talent Research Start-Up Project Funding of Henan Academy of Sciences (Grant No. 241819112) and the Natural Science Foundation of Henan Province (Grant No. 252300420903).
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