8 problems

Fix $\lambda<0$ and consider the 4-dimensional space of local $\textup{SU}(3)$-invariant shrinkers, together with the complete AC shrinkers among them on $\Lambda^2_-\mathbb{CP}^2$…

Let $\Lambda^2_-\mathbb{S}^4$ be the anti-self-dual bundle of the 4-sphere, and let the explicit AC shrinker be the complete $\textup{Sp}(2)$-invariant shrinker described in Exampl…

Let $\Lambda^2_-\mathbb{S}^4$ be the anti-self-dual bundle of the 4-sphere, and consider complete AC $\textup{Sp}(2)$-invariant Laplacian shrinkers on it. The explicit shrinker is…

The space of $\textup{SU}(3)$-invariant closed $\textup{G}_2$-cones is 2-dimensional. Consider the subset consisting of cones that occur as asymptotic cones of $\textup{SU}(3)$-inv…

Let $\Lambda^2_-\mathbb{CP}^2$ denote the anti-self-dual bundle of the complex projective plane. A complete expander has quadratic-exponential volume growth when its volume grows a…

Consider complete AC shrinkers with $\textup{SU}(3)$ symmetry on the relevant cohomogeneity-one $\textup{SU}(3)$-invariant geometry. SU(3)-invariant shrinker-finiteness conjecture.…

Let $\Lambda^2_-\mathbb{CP}^2$ be the anti-self-dual bundle of the complex projective plane. An AC expander or shrinker is a complete Laplacian-flow expanding or shrinking soliton…

Let $\Lambda^2_-\mathbb{CP}^2$ denote the anti-self-dual bundle of the complex projective plane, equipped with the natural $\textup{SU}(3)$-action. An expander is a Laplacian-flow…