5 problems

Let $M$ be a complete noncompact (open) Riemannian manifold with nonnegative Ricci curvature. For a fixed growth rate, consider the vector space of harmonic functions on $M$ with p…

Let $M$ be an open manifold with nonnegative Ricci curvature, and consider the vector space of biharmonic functions on $M$, where biharmonic means satisfying … For a fixed growth r…

Let $M$ be an open manifold with nonnegative Ricci curvature, and let $u$ be a bounded biharmonic function on $M$, meaning that $abla^4 u=0$ in the source's terminology via the bi…

Let $M$ be the surface setting of the main theorem, so $n=2$, and let the theorem's other hypotheses and notation remain in force. Surface-case conjecture. Theorem 1.1 holds withou…

Topping's Ricci-flow existence conjecture. The Ricci flow equation