Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
Default functions and Liouville type theorems based on symmetric diffusions
Atsushi Atsuji
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Keywords: Brownian motion on manifolds, strictly local submartingale, subharmonic function, 𝐿1-Liouville theorem, Liouville theorem for holomorphic maps
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2021 Volume 73 Issue 2 Pages 525-551

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Abstract

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.

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