On the generic eigenvalue flow of a family of metrics and its application (Q1293487)

Let \( M \) be a compact manifold with \( \partial M = \emptyset \) and \( g(t) \) a family of metrics on \( M \) depending continuously on the parameter \( t\). The author defines a generic eigenvalue flow associated to \( g(t) \) and proves that the corresponding eigenfunction is continuous with respect to the parameter \( t\). Then he applies this result to the study of the polynomial growth of the harmonic functions on a complete manifold.