3 problems

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…

Van Lujik's conjecture. The Hodge-number parameter satisfies $q=0$.

Let the cuboid be $[-a,a]\times[-b,b]\times[-1,1]$, with $a,b\leq 1$, and consider the surface plotting its first Steklov invariant in the first octant. Differentiability and origi…