We consider the problem of existence of the extreme points and support points of harmonic -Bloch mappings and little harmonic -Bloch mappings. First, we prove a necessary condition for a little harmonic -Bloch mapping to be an extreme point of the unit ball of the normalized little harmonic -Bloch spaces in the unit disk , and we also show that a harmonic -Bloch unit-valued set consists of several simple closed pairwise disjoint analytic curves and several isolated points. Then we show that a harmonic -Bloch mapping is a support point of the unit ball of the normalized harmonic -Bloch spaces in if and only if the -Bloch unit-valued set of is not empty. We also give a characterization for the support points of the unit ball of the harmonic -Bloch spaces in .
"Extreme points and support points of harmonic $\alpha$-Bloch mappings." Rocky Mountain J. Math. 50 (4) 1323 - 1354, August 2020. https://doi.org/10.1216/rmj.2020.50.1323