6 problems

The preceding discussion concerns the case in which the concave term $h$ is removed from the definition of $f$. Extension conjecture. Similar statements should be provable with $h$…

Let $S^1=\{y\in\mathbb{R}^2\mid y_1^2+y_2^2=1\}$, and let $\mathfrak{B}^\circ_\delta[f]$ and $\mathfrak{B}^{\circ,*}_\delta[f]$ denote, respectively, the minimal locally concave an…

Generalized-cone extremal conjecture.

Avkhadiev–Wirths' coefficient conjecture. For every $f\in CO(2)$ and every integer $n\geq 2$,

Lieb–Solovej's extended conjecture. The minimization property of the Wehrl entropy continues to hold when $f(x)=-x\ln x$ is replaced by any concave function: $S_f(v)$ is minimized…

Let $\alpha\in(1,2)$, let $CO_H(\alpha)$ be the class of harmonic mappings $f=h+\overline{g}$ in ${\mathbb D}$ whose analytic part $h$ belongs to the class $CO(\alpha)$ of concave…