Tropical Nevanlinna theory of several variables

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 (holomorphic maps) in several 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 nondegenerate tropical holomorphic maps f with subnormal growth from Rⁿ into tropical projective space TP^m intersecting tropical hypersurfaces \V₏䲛\₉=₁^q with degree d₉, we then obtain the Second Main Theorem \|\, \, \, (q-M-1-λ) Tf (r) ₉=₌+₂q 1dⱼN (r, 1ₓ Pⱼ f) + o (Tf (r) ), where d=lcd (d₁, , dₐ) and M= (d^m+d) -1.