Steklov eigenvalue problem on orbisurfaces

 The Steklov eigenvalue problem is an eigenvalue problem whose spectral parameters appear in the boundary condition. On a Riemannian surface with smooth boundary, Steklov eigenvalues have a very sharp asymptotic expansion. Also, a number of interesting sharp bounds for the $k$th Steklov eigenvalues have been known. We extend these results on orbisurfaces and discuss how the structure of orbifold singularities comes into play. This is joint work with Arias-Marco, Dryden, Gordon, Ray and Stanhope.