3 papers
math.AP2021
Bloch Waves in High Contrast Electromagnetic Crystals
Robert Lipton, Robert Viator, Silvia Jimenez Bolanos +1
Analytic representation formulas and power series are developed describing the band structure inside non-magnetic periodic photonic three-dimensional crystals made from high dielec…
math.SP2021
Steklov Eigenvalues of Nearly Spherical Domains
Robert Viator, Braxton Osting
We consider Steklov eigenvalues of three-dimensional, nearly-spherical domains. In previous work, we have shown that the Steklov eigenvalues are analytic functions of the domain pe…
math.AP2019
Analyticity of Steklov eigenvalues of nearly-circular and nearly-spherical domains
Robert Viator, Braxton Osting
We consider the Dirichlet-to-Neumann operator (DNO) on nearly-circular and nearly-spherical domains in two and three dimensions, respectively. Treating such domains as perturbation…