I will outline work with Jess Ratzkin at University of Cape Town on a Rayleigh quotient that interpolates between that for torsional rigidity and that for principal frequency. I will also discuss a Schwarz Lemma for principal frequency due to Laugesen and Morpurgo which is related to work of Burckel, Marshall, Minda, Poggi-Corradini and Ransford on versions of Schwarz's Lemma.