Stable solution of the Logarithmic Minkowski problem in the case of hyperplane symmetries

The logarithmic Minkowski conjecture and the Lp-Minkowski problem

“…In some cases when uniqueness of the solution of the Log-Minkowski problem is known, even the stability of the solution has been established. For example, Böröczky, De [40] established this among convex bodies invariant under n given reflections through linear hyperplanes. Concerning Firey's classical result that the only origin symmetric solution of the Log-Minkowski problem (21) with constant f is the centered ball, Ivaki [156] verified a stability version.…”

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

“…In some cases when uniqueness of the solution of the Log-Minkowski problem is known, even the stability of the solution has been established. For example, Böröczky, De [39] established this among convex bodies invariant under n given reflections through linear hyperplanes. Concerning Firey's classical result that the only origin symmetric solution of the Log-Minkowski problem (20) with constant f is the centered ball, Ivaki [146] verified a stability version.…”

On subspace concentration for dual curvature measures

“…where ν K (•) is the spherical image map (see Section 2), essentially the Gauss map on the regular boundary points of K. The characterization of the cone volume measure is known as the logarithmic Minkowski problem. It has been studied extensively over the last few years in many different contexts, see, e.g., [3,4,5,6,7,8,10,14,25,32,43,44,46], and for results in the general L p setting see, e.g., [2,15,23,29].…”