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math.DG2026
Nonlinear Bochner-Kodaira-Nakano identity and nonlinear Hodge correspondence for morphisms
Nianzi Li, Mao Sheng
We establish a nonlinear Bochner-Kodaira-Nakano identity for sections of complex fiber bundles. As applications, we obtain a nonlinear Bochner-type vanishing theorem for holomorphi…
math.AG2026
Uniformization as Tannakian Reconstruction
Xiaojin Lin, Mao Sheng
Classical hyperbolic uniformization identifies every hyperbolic log-orbi curve with a compactified quotient of the upper half-plane by a cofinite Fuchsian lattice. The lattice is u…
math.DG2026
Connections, metrics and Higgs fields on complex fiber bundles
Nianzi Li, Mao Sheng
We give a differential-geometric representation of the extension class associated to a holomorphic fibration, generalizing the work of Atiyah on holomorphic principal bundles in a…