6 problems

Let two flat surfaces be equipped with their Steklov spectra. Flat inverse Steklov spectral conjecture. Two flat surfaces are Steklov isospectral if and only if they are isometric.…

Jollivet–Sharafutdinov inverse Steklov spectral conjecture. The metrics $g_1$ and $g_2$ have the same Steklov spectrum if and only if they are $\sigma$-isometric. This conjecture i…

Let $P$ be a convex polygonal domain, and let $\Omega$ be a simply-connected smoothly bounded domain. Two domains are Steklov isospectral if their Steklov spectra, counted with mul…

Let $\Sigma$ be a compact surface, let $c$ be a conformal class on $\Sigma$, and let $\sigma^*_1(\Sigma,c)$ denote the normalized first Steklov eigenvalue in that conformal class.…

Let $\Sigma$ be a compact surface, and let $I^\sigma_k(\Sigma)$ denote the infimum of the normalized $k$-th Steklov eigenvalue over conformal classes on $\Sigma$. Attainment conjec…

Let a cuboid be a Euclidean rectangular box, and let two cuboids be Steklov isospectral when their Steklov spectra, counted with multiplicities, coincide. Steklov spectral determin…