Poincaré–Lelong equation via the Hodge–Laplace heat equation
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Publication:5396110
DOI10.1112/S0010437X12000322zbMath1286.53048arXiv1109.6102OpenAlexW2024582609WikidataQ126101527 ScholiaQ126101527MaRDI QIDQ5396110
Publication date: 5 February 2014
Published in: Compositio Mathematica (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1109.6102
Asymptotic behavior of solutions to PDEs (35B40) Heat equation (35K05) Kähler manifolds (32Q15) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Heat and other parabolic equation methods for PDEs on manifolds (58J35)
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Cites Work
- An optimal gap theorem
- Poisson equation, Poincaré-Lelong equation and curvature decay on complete Kähler manifolds.
- Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature.
- Vanishing theorems on complete Kähler manifolds and their applications
- The heat equation and harmonic maps of complete manifolds
- On the existence of solutions of Poisson equation and Poincaré-Lelong equation
- Holomorphic bisectional curvature
- Sharp differential estimates of Li-Yau-Hamilton type for positive (p, p) forms on Kähler manifolds
- Poisson equation and Hermitian-Einstein metrics on vector bundles over complete noncompact Kahler manifolds
- A monotonicity formula on complete Kähler manifolds with nonnegative bisectional curvature
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