Abstract
This paper aims to consider the dual Brunn–Minkowski inequality for log-volume of star bodies, and the equivalent Minkowski inequality for mixed log-volume.
Highlights
The classical Brunn–Minkowski theory, known as the theory of mixed volumes, is the core theory in convex geometric analysis
When μ is a spherical Lebesgue measure of Sn–1, by the equality condition of LpMinkowski inequality, we have that the equality holds if and only if K and L are dilates of each other
Proof Since we have proved the Lp-Brunn–Minkowski inequality by the Lp-Minkowski inequality, we only need to prove the Lp-Minkowski inequality by the Lp-Brunn–Minkowski inequality
Summary
The classical Brunn–Minkowski theory, known as the theory of mixed volumes, is the core theory in convex geometric analysis. We prove the dual Brunn–Minkowski inequality for the log-volume μ(K) of the star body K , and the equivalent Minkowski inequality for mixed log-volume. Lemma 3.1 Let μ be the spherical Lebesgue measure of Sn–1.
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