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• W2895506329 abstract "In this paper, we introduce a new energy density function $mathscr Y$ on the projective bundle $mathbb{P}(T_M)>M$ for a smooth map $f:(M,h)>(N,g)$ between Riemannian manifolds $$mathscr Y=g_{ij}f^i_alpha f^j_beta frac{W^alpha W^beta}{sum h_{gammadelta} W^gamma W^delta}.$$ We get new Hessian estimates to this energy density and obtain various new Liouville type theorems for holomorphic maps, harmonic maps and pluri-harmonic maps. For instance, we show that there is no non-constant holomorphic map from a compact emph{Hermitian manifold} with positive (resp. non-negative) holomorphic sectional curvature to a emph{Hermitian manifold} with non-positive (resp. negative) holomorphic sectional curvature." @default.
• W2895506329 created "2018-10-12" @default.
• W2895506329 creator A5030350248 @default.
• W2895506329 date "2018-10-08" @default.
• W2895506329 modified "2023-09-26" @default.
• W2895506329 title "RC-positivity and the generalized energy density I: Rigidity" @default.
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• W2895506329 doi "https://doi.org/10.48550/arxiv.1810.03276" @default.
• W2895506329 hasPublicationYear "2018" @default.
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