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On a generalised Blaschke-Santal\`o inequality

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arxiv 1808.02218 v1 pith:BXD6T4FU submitted 2018-08-07 math.AP math.DG

Haodi Chen This is my paper · ORCID
classification math.APmath.DG
keywords inequalityblaschke-santalconvexgeneralisedargumentbodiesbodybound
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abstract

In this paper, we establish a generalised Blaschke-Santal\`o inequality for convex bodies in $\mathbb R^{n+1}$. This inequality gives an upper bound estimate for the product of dual quermassintegrals of convex body and its polar set. Our argument is based on induction on dimensions.

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  1. Compactness of the $L_p$ dual Minkowski problem in $\mathbb{R}^3$

    math.AP 2025-05 conditional novelty 7.0 of 10

    For convex bodies in R^3, bounded L_p qth dual curvature with p in [0,1) and q>2+p forces a uniform diameter upper bound and volume lower bound.

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