5 papers
Spectral rigidity of two-dimensional Liouville tori
Joscha Henheik, Vadim Kaloshin, Yunzhe Li +1
It is a folklore conjecture that Liouville metrics are the only Riemannian metrics with integrable geodesic flow on the two-dimensional torus. In this paper, we study Laplace-isosp…
Silent Orbits and Cancellations in the Wave Trace
Illya Koval, Amir Vig
This paper shows that the wave trace of a bounded and strictly convex planar domain may be arbitrarily smooth in a neighborhood of some point in the length spectrum. In other words…
Balian-Bloch Wave Invariants for Nearly Degenerate Orbits
Vadim Kaloshin, Illya Koval, Amir Vig
This paper is part I of a series in which we aim to show that the singular support of the wave trace and the length spectrum of a smooth, strictly convex, and bounded planar billia…
The Wave Trace and Birkhoff Billiards
Amir Vig
The purpose of this article is to develop a Hadamard-Riesz type parametrix for the wave propagator in bounded planar domains with smooth, strictly convex boundary. This parametrix…
Robin Spectral Rigidity of the Ellipse
Amir Vig
In this paper, we investigate isospectral deformations of the ellipse with Robin boundary conditions, allowing both the Robin function and domain to deform simultaneously. We…