6 problems

A gradient Yamabe soliton is a Riemannian manifold $(M^n,g)$ equipped with a smooth function $F$ and a constant $\lambda\in\mathbb{R}$ satisfying … where $R$ is the scalar curvatur…

Constant-curvature packing conjecture. If

Let $(g(t))_{t\in[0,T]}$ be an instantaneously complete, conformally hyperbolic Yamabe flow on $(\mathbb{H},g_{\mathbb{H}})$, where $m$ denotes the dimension of the hyperbolic spac…

Luo's convergence conjecture. The discrete Yamabe flow will converge to the constant curvature PL-metric after a finite number of surgeries on the triangulation.

Let $(M^3,J,\mathring{\theta})$ be a closed spherical CR $3$-manifold with positive Tanaka-Webster scalar curvature and vanishing torsion. Consider the normalized CR Yamabe flow st…

Let $M^3$ be a three-dimensional complete Riemannian manifold satisfying the Ricci pinching condition … where $epsilon>0$ is a uniform constant. Hamilton's compactness conjecture.…