Rigidity is established for isotropic harmonic maps from the 2-torus to CP space arising from complete linear systems, and for broader holomorphic embeddings lacking hyperosculation points when Fubini-Study pullbacks satisfy an extra condition.
Ballmann,Lectures on K¨ ahler Manifolds, vol
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Establishes lower bound for Kähler hyperbolicity modulus on complete Kähler manifolds via boundary gradient length of plurisubharmonic functions, with applications to symmetric and strongly pseudoconvex domains.
Survey of known results on the bottom of the spectrum of the Hodge Laplacian on complete noncompact Kähler manifolds, including upper bounds under curvature assumptions and rigidity theorems.
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K\"ahler Hyperbolicity Modulus for Simply-connected K\"ahler Hyperbolic manifolds
Establishes lower bound for Kähler hyperbolicity modulus on complete Kähler manifolds via boundary gradient length of plurisubharmonic functions, with applications to symmetric and strongly pseudoconvex domains.
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Bottom of the spectrum of complete noncompact K\"{a}hler manifolds
Survey of known results on the bottom of the spectrum of the Hodge Laplacian on complete noncompact Kähler manifolds, including upper bounds under curvature assumptions and rigidity theorems.