6 problems

Let $G$ be a connected semisimple Lie group with maximal compact subgroup $K$ and minimal parabolic subgroup $P$. The symmetric space is $K\backslash G$, and its Furstenberg bounda…

Let $X$ be a rank-one symmetric space of noncompact type, let $\lambda\in\mathbb{C}$ satisfy $\operatorname{Im}(\lambda)=0$ with $\lambda\neq 0$, and let $u\in C^\infty(X)$ satisfy…

Let $G$ be a connected real semisimple noncompact Lie group with finite center, $K$ a maximal compact subgroup, and $X=G/K$. Let $G=KAN$ be an Iwasawa decomposition, let $M$ be the…

Let $G/K$ be a Riemannian symmetric space with $\rho$ the half-sum of positive restricted roots, let $\mathfrak{a}_{\mathbb{C}}^*$ be the complexified dual of a maximal abelian sub…

Sharpness and optimizer conjecture. There exists a sharp constant $C>0$ such that

Helgason's conjecture. For $\operatorname{Re}\lambda\in\overline{\mathfrak j^*_+}$, the Poisson transform is a bijection.