4 problems

Min-max uniqueness conjecture. Under a certain metric on $\mathbb{RP}^3$, every minimal real projective plane constructed via min-max could be the same area-minimizing one, with po…

Point-plus-connected clean-intersection conjecture. The only such example is $C=\mathbb{RP}^{n-1}$, at least up to homotopy-equivalence, and one always has $\mu(p)\in\\{0,n\\}$.

Clean-intersection homotopy conjecture. The manifold $C$ must be at least homotopy-equivalent to $\mathbb{RP}^{n-1}$.

Let ${\mathbb{RP}}^n$ be real projective space with round metric $g$, and let $wg$ be a conformally equivalent metric whose volume is normalized by … Write $\lambda_2(w)$ for the s…