Convergence of Scalar Curvature of Long Time K\"ahler-Ricci Flow on K\"ahler Manifold

Lei Zhang; Zhenlei Zhang

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arXiv · 2606.17402

Convergence of Scalar Curvature of Long Time K\"ahler-Ricci Flow on K\"ahler Manifold

Lei Zhang·Zhenlei Zhang

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Abstract

This paper is concerned with a class of the long time K\"ahler-Ricci flow on a compact K\"ahler manifold. It is shown that the uniform $\mu$-entropy or uniform Sobolev inequality along the normalized K\"ahler-Ricci flow with semiample canonical bundle. As a consequence, we prove that the scalar curvature of the K\"ahler metrics along the normalized K\"ahler-Ricci flow converge to negative Kodaira dimension of the compact K\"ahler manifold.

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BibTeX RIS

Lei Zhang, Zhenlei Zhang. 2026-06-16. Convergence of Scalar Curvature of Long Time K\"ahler-Ricci Flow on K\"ahler Manifold. https://arxiv.org/abs/2606.17402

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