4 papers
Lens rigidity in 2D: The reconstruction of a Riemann surface from its geodesic lengths
Spyros Alexakis, Matti Lassas
We address the question of whether a Riemannian manifold-with-boundary (M,g) in dimension two is uniquely determined from knowledge of the distances between points on its boundary.…
Evaluating singular and near-singular integrals on smooth surfaces with quadratic geometric approximation and closed form expressions
Andrew Zheng, Spyros Alexakis, Adam R Stinchcombe
Most Fredholm integral equations involve integrals with weakly singular kernels. Once the domain of integration is discretized into flat triangular elements, these weakly singular…
Inverse scattering problems for non-linear wave equations on Lorentzian manifolds
Spyros Alexakis, Hiroshi Isozaki, Matti Lassas +1
We show that an inverse scattering problem for a semilinear wave equation can be solved on a manifold having an asymptotically Minkowskian infinity, that is, scattering functionals…
Existence of static vacuum extensions for Bartnik boundary data near Schwarzschild spheres
Spyros Alexakis, Zhongshan An, Ahmed Ellithy +1
We obtain existence and local uniqueness of asymptotically flat, static vacuum extensions for Bartnik data on a sphere near the data of a sphere of symmetry in a Schwarzschild mani…