AI 中文总结
研究凯勒流形上热方程正解的黑塞矩阵上界，通过证明全局和局部上界及改进韩和张的结果，将双边曲率界下的上界扩展到截面曲率有下界的黎曼流形。
AI 中文摘要
我们证明了在双截曲率有下界的凯勒流形上热方程正解的黑塞矩阵的全局和局部上界。我们还通过弱化韩和张在黎曼流形上黑塞估计中的曲率假设改进了他们的一个结果。具体而言，我们将他们最初在双边曲率界下得到的全局和局部上界扩展到了截面曲率有下界的黎曼流形上。
英文摘要
We prove global and local upper bounds for the Hessian matrices of positive solutions to the heat equation on Kähler manifolds whose bisectional curvature is bounded from below. We also improve a result of Han and Zhang by weakening the curvature assumptions in their Hessian estimates on Riemannian manifolds. More precisely, we extend their global and local upper bounds, originally obtained under two-sided curvature bounds, to Riemannian manifolds with sectional curvature bounded from below.
