Henrik Matthiesen

Small eigenvalues of surfaces of finite type

Extending our previous work on eigenvalues of closed surfaces and work of Otal and Rosas, we show that a complete Riemannian surface

On the analytic systole of Riemannian surfaces of finite type

S

Existence of metrics maximizing the first eigenvalue on closed surfaces

of finite type and Euler characteristic

On the bottom of spectra under coverings

\unicode[STIX]{x1D712}(S)<0

Small eigenvalues of closed surfaces

has at most

The systole of large genus minimal surfaces in positive Ricci curvature.

-\unicode[STIX]{x1D712}(S)

Monotonicity results for the first Steklov eigenvalue on compact surfaces

small eigenvalues.

Bottom of spectra and amenability of coverings

In (J Differ Geom 103(1):1–13, 2016) we introduced, for a Riemannian surface S, the quantity

Small eigenvalues of surfaces - old and new

{\Lambda(S):={\rm \inf}_F\lambda_0(F)}