A fundamental question in Differential Geometry which has spurred much recent work is whether every orientable compact surface with boundary can be minimally embedded in the Euclidean 3-ball with free boundary. I will discuss work (joint with M. Karpukhin, R. Kusner, and D. Stern) which resolves this problem.
In this talk, I will introduce a novel Riemannian geometric model for wave propagation in gas giant planets. Terrestrial planets and gas giants have one key difference: in gas, density goes to zero at the surface, and seismic waves come to a full stop. We model the sound speed in a planet by a Riemannian…
We start by giving a short introduction to geometric inverse problems. Then we present our recent results regarding inverse problems for the minimal surface equation. Minimal surfaces are solutions to a quasilinear elliptic equation. We determine a minimal surface up to an isometry from the corresponding Dirichlet-to-Neumann map in dimension 2. Applications of the results…
The structure of algebras of differential invariants, particularly their generators, is based on the symbolic invariant calculus provided by the method of equivariant moving frames. I will discuss a new computational algorithm that will, in many cases, determine whether a given set of differential invariants is generating. As an example, we establish a new result…