Banachraum

The general question in this talk is whether eigenvalues of operators defined on geometric spaces converge as these spaces converge to a limit space. Because the operators that we consider are often nonlinear, we need proper generalizations of eigenvalues, such as Krasnoselskii eigenvalues. I'll describe how to obtain continuity for eigenvalues of the Laplace operator defined on CD(K,N) spaces under measured Gromov-Hausdorff convergence, and I will explain how to get semicontinuity of Krasnoselskii eigenvalues under volume flat convergence. The talk contains results from joint works with Luigi Ambrosio, Shouhei Honda, Jeff Jauregui and Raquel Perales.

Jacobus Portegies

Eindhoven