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.
Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric
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abstract
We shall show that $q$-semipositivity of the vector bundle $E$ over a K\"ahler total space $\mathcal X$ implies the Griffiths-semipositivity of the $q$-th direct image of $\mathcal O(K_{\mathcal X/B}\otimes E)$. As an application, we shall give a negative-curvature criterion for the generalized Weil-Petersson metric on the base manifold.
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math.DG 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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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.