An upper estimate of the new curvature entropy is provided, via the integral inequality of a concave function. For two origin-symmetric convex bodies in $\mathbb{R}^n$, this bound is sharper than the log-Minkowski inequality of curvature entropy. As its application, a novel proof of the log-Minkowski inequality of curvature entropy in the plane is given.
Deyi LI
,
Lei MA
,
Chunna ZENG
. NOTES ON THE LOG-MINKOWSKI INEQUALITY OF CURVATURE ENTROPY[J]. Acta mathematica scientia, Series B, 2025
, 45(1)
: 16
-26
.
DOI: 10.1007/s10473-025-0102-1
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