Abstract: The only known class of integrable metrics on the 2-torus is the so-called Liouville metrics, i.e. Riemannian metrics of the form (f(x) + g(y)) (dx^2 + dy^2). We study the deformations of Liouville metrics within the same conformal class by trigonometric polynomials. We show that a generic Liouville metric is spectrally rigid under such deformations. This is a joint work with Joscha Henheik, Vadim Kaloshin and Amir Vig.
Deformational spectral rigidity of Liouville metrics
16.05.2025 15:16 - 16:16
Organiser:
H. Bruin, R. Zweimüller
Location:
ISTA