Pacific Institute for the Mathematical Sciences - PIMS

Determinants of Laplacians as functions on spaces of metrics

The determinant of the Laplacian is a global Riemannian invariant which
is defined formally as the product of the nonzero eigenvalues of the
Laplacian of a given Riemannian metric. It gives a continuous function
on the space of Riemannian metrics. In this talk we are interested in
the case of compact surfaces with boundary and will discuss the
properness of the determinant function on the moduli space of
hyperbolic surfaces with geodesic boundary and on the moduli space of
flat surfaces with boundary of constant geodesic curvature. We will
also discuss an application to the following isospectral compactness
problem: On a given compact surface with boundary, consider the set of
all smooth flat metrics having the same Dirichlet Laplacian spectrum.
Is it compact in C^\infty topology?

3:30pm, WMAX 110