Correction to: Functional John and Löwner conditions for pairs of log-concave functions

Correction to definitionsDefinition 1.4 on p.20618 (corrected).For two functions f , g : R d → R , their set of contact pairs iswhere C eq and C bz denote 'equal' and 'boundary zero' contact pairs, namely,Here, N A, u denotes the Fréchet normal cone of A ⊂ R d+1 at a point u ∈ R d+1 ; see Definition 2.2.Explanation .In the published version, C f , g excluded those contacts of the liftings of f and g , where f (u) = g (u) .The definition above includes some of these points: those, whose last coordinate is zero.Without these corrections, Theorems 1.3, 1.5 and 1.7 are formally incorrect as stated.