Abstract
We prove the existence of a family of non-trivial solutions of the Liouville equation in dimensions two and four with infinite volume. These solutions are perturbations of a finite-volume solution of the same equation in one dimension less. In particular, they are periodic in one variable and decay linearly to −∞ in the other variables. In dimension two, we also prove that the periods are arbitrarily close to πk,k∈N (from the positive side). The main tool we employ is bifurcation theory in weighted Hölder spaces.
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