2 problems

Ellipse-hole eigenvalue monotonicity conjecture. The eigenvalues $\sigma_1(\Omega_{(t_1,t_2)})$ and $\mu_2(\Omega_{(t_1,t_2)})$ decrease with respect to the distance between the ce…

Ball-hole eigenvalue monotonicity conjecture. The first and second nonzero Steklov eigenvalues $\sigma_1(\Omega_{(t_1,t_2)})$ and $\sigma_2(\Omega_{(t_1,t_2)})$ decrease as the dis…