10 problems

The flow starts from initial data that are not necessarily convex; the phenomenon under discussion is blow-up of curvature in finite time. Finite-time curvature blow-up conjecture.…

Complete-graph curvature flow conjecture. If $P_0$ is a non-degenerate Markovian weighting scheme without laziness on the complete graph $K_n$ with $n \ge 2$, then the curvature fl…

Curvature flow convergence conjecture. The curvature flow converges for any initial condition $(G,P_0)$, that is, $(G,P(t))$ has a well-defined limit

Let $\mathcal M$ be a cone and let a closed curve on $\mathcal M$ be not homotopic to a point on $\mathcal M$. Elliott's conjecture. Under geodesic curvature flow, the curve will c…

HCF pinching conjecture. Under the HCF, any induced metric on such a manifold pinches towards the HCF-Einstein metric.

Let $\hat{\Omega}$ be curvature flow on embedded graphs in $\mathbb{R}^n$, rescaled so that a characteristic length scale remains equal to one, and let $\mathcal{G}^n$ be the class…

Let $\mathcal{G}^n$ be the class of embedded graphs in $\mathbb{R}^n$. Suppose $G\in\mathcal{G}^n$ is an embedded graph with a homogeneous topological cloth and a well-defined time…

A network flow is a curvature flow on embedded graphs, with singular times at which the flow is understood through varifold convergence. In two dimensions, a connected collection o…

Let $G(s,t)$ be the negatively curved metric on the solid torus evolved by cross curvature flow with the time-dependent Dirichlet boundary conditions described in the source, and l…

Let $M$ be a $3$-manifold with a metric whose sectional curvatures are strictly negative, and let $\textsc{xcf}$ denote cross curvature flow. Hamilton–Chow conjecture. After suitab…