4 problems

Consider minimal surfaces in $\mathbb{S}^3$ with area less than $8\pi$, and take the boundary of this space with respect to the varifold topology. A sequence whose areas tend to…

Mixed-Neumann spectral conjecture. For every metric $g$ on $\Omega_k$,

Let $\eta_{t,x(t)}$ be the family of DPW potentials described in the paper, and let $\psi(t)$ be the reparametrization relating it to the analytic family of potentials producing th…

Kusner–Pinkall conjecture. The area $A(\Sigma_{g,L})$ is monotonically increasing as a function of $g$, and