The affine log-Aleksandrov–Fenchel inequality
DOI:
https://doi.org/10.33044/revuma.2620Abstract
We establish a new affine log-Aleksandrov–Fenchel inequality for mixed affine quermassintegrals by introducing new concepts of affine and multiple affine measures, and using the newly established Aleksandrov–Fenchel inequality for multiple mixed affine quermassintegrals. Our new inequality yields as special cases the classical Aleksandrov–Fenchel inequality and the $L_{p}$-affine log-Aleksandrov–Fenchel inequality. The affine log-Minkowski and log-Aleksandrov–Fenchel inequalities are also derived.
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