Asian Journal of Mathematics

Volume 27 (2023)

Number 1

Nevanlinna-type theory based on heat diffusion

Pages: 77 – 94



Xianjing Dong (School of Mathematical Sciences, Qufu Normal University, Qufu, China)


We obtain an analogue of Nevanlinna theory of holomorphic mappings from a complete and stochastically complete Kähler manifold into a complex projective manifold. When certain curvature conditions are imposed, some Nevanlinna-type defect relations based on heat diffusion are established.


Nevanlinna theory, second main theorem, defect relation, heat diffusion, Ricci curvature

2010 Mathematics Subject Classification

30D35, 32H30

Received 21 May 2020

Accepted 13 December 2022

Published 16 June 2023