The Logarithmic Minkowski conjecture and the $L_p$-Minkowski Problem

Karoly J. Boroczky

The Logarithmic Minkowski conjecture and the $L_p$-Minkowski Problem

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arxiv 2210.00194 v3 pith:5FX4R4HE submitted 2022-10-01 math.AP math.MG

Karoly J. Boroczky This is my paper · ORCID

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keywords minkowskiconjecturelogarithmicproblemcaseconcerningconnectionscurrent

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abstract

The current state of art concerning the $L_p$ Minkowski problem as a Monge-Ampere equation on the sphere and Lutwak's Logarithmic Minkowski conjecture about the uniqueness of even solution in the $p=0$ case are surveyed and connections to many related problems are discussed.

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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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