Default functions appear when one discusses conditions which ensure that a local martingale is a true martingale. We show vanishing of default functions of Dirichlet processes enables us to obtain Liouville type theorems for subharmonic functions and holomorphic maps.
Partially supported by the Grant-in-Aid for Scientific Research 17K18741, Japan Society for the Promotion of Science.
"Default functions and Liouville type theorems based on symmetric diffusions." J. Math. Soc. Japan 73 (2) 525 - 551, April, 2021. https://doi.org/10.2969/jmsj/82398239