Tropical Nevanlinna theory in several variables

Abstract The main goal of this paper is to establish the higher dimensional Nevanlinna theory in tropical geometry. We first develop a theory of tropical meromorphic functions (tropical holomorphic maps) in several real variables, such as the proximity function, counting function and characteristic function, the first main theorem, higher dimensional tropical versions of the logarithmic derivative lemmas. Based on this, for algebraically non‐degenerate tropical holomorphic maps with subnormal growth from into tropical projective space intersecting tropical hypersurfaces with degree , we then obtain the second main theorem where and . Our work in this paper significantly generalizes previous results by Korhonen–Tohge [Adv. Math. 298 (2016), 693–725] and Cao–Zheng [Ann. Sc. Norm. Super. Pisa Cl. Sci. 26 (2025), no. 4, 2105–2144].