In this paper,we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of the development of curves.
In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application ...In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.展开更多
基金partially supported by GDNSF(2021A1515010264)NNSF of China(11571215)。
文摘In this paper,we extend the classical de Rham decomposition theorem to the case of Riemannian manifolds with boundary by using the trick of the development of curves.
基金partially supported by the Yangfan project from Guangdong ProvinceNSFC(11571215)
文摘In this article, we obtain Li-Yau-type gradient estimates with time dependent parameter for positive solutions of the heat equation that are different with the estimates by Li-Xu [21] and Qian [23]. As an application of the estimate, we also obtained slight improvements of Davies' Li-Yau-type gradient estimate.
