Existence of metrics maximizing the first eigenvalue on closed surfaces

Seminar series

Partial Differential Equations Seminar

Date

Mon, 13 Nov 2017
16:00

Location

Speaker

Anna Siffert

Organisation

MPI Bonn

We prove that for closed surfaces of fixed topological type, orientable or non-orientable, there exists a unit volume metric, smooth away from finitely many conical singularities, that
maximizes the first eigenvalue of the Laplace operator among all unit volume metrics. The key ingredient are several monotonicity results, which have partially been conjectured to hold before. This
is joint work with Henrik Matthiesen.