85 citations · 285 across the 40 of their papers we have counts for
7 papers · 1 filter
Flat tori with large Laplacian eigenvalues in dimensions up to eight
Chiu-Yen Kao, Braxton Osting, Jackson C. Turner
We consider the optimization problem of maximizing the -th Laplacian eigenvalue, , over flat -dimensional tori of fixed volume. For , this problem is equivalent t…
An Isoperimetric Sloshing Problem in a Shallow Container with Surface Tension
Chee Han Tan, Christel Hohenegger, Braxton Osting
In 1965, B. A. Troesch solved the isoperimetric sloshing problem of determining the container shape that maximizes the fundamental sloshing frequency among two classes of shallow c…
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…
Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems
Chiu-Yen Kao, Braxton Osting, Èdouard Oudet
Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary mini…
Computational Methods For Extremal Steklov Problems
Eldar Akhmetgaliyev, Chiu-Yen Kao, Braxton Osting
We develop a computational method for extremal Steklov eigenvalue problems and apply it to study the problem of maximizing the -th Steklov eigenvalue as a function of the domain…
Spectrally Optimized Pointset Configurations
Braxton Osting, Jeremy L. Marzuola
The search for optimal configurations of pointsets, the most notable examples being the problems of Kepler and Thompson, have an extremely rich history with diverse applications in…
An Isoperimetric inequality for an integral operator on flat tori
Braxton Osting, Jeremy L. Marzuola, Elena Cherkaev
We consider a class of Hilbert-Schmidt integral operators with an isotropic, stationary kernel acting on square integrable functions defined on flat tori. For any fixed kernel whic…