本文研究了在Bakry-Émery Ricci曲率条件下加权Laplace算子的Li-Yau梯度估计的问题,利用Bochner公式与加权Laplace公式以及极大值定理等处理Li-Yau梯度问题的方法,获得了加权Laplace在Bakry-Émery Ricci曲率有下界的条件下,...本文研究了在Bakry-Émery Ricci曲率条件下加权Laplace算子的Li-Yau梯度估计的问题,利用Bochner公式与加权Laplace公式以及极大值定理等处理Li-Yau梯度问题的方法,获得了加权Laplace在Bakry-Émery Ricci曲率有下界的条件下,热方程的正解u (x, t)的最优Li-Yau梯度估计。In this paper, the problem of Li-Yau gradient estimation of weighted Laplace operator under Bakry-Émery Ricci curvature is studied. Bochner formula, weighted Laplace formula and the maximum theorem are used to deal with the Li-Yau gradient problem. The optimal Li-Yau gradient estimation for the positive solution u (x, t) of the heat equation is obtained under the condition of lower bound for weighted Laplace Bakry-Émery Ricci curvature.展开更多
In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to b...In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.展开更多
This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature...This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.展开更多
This paper explores the pivotal role of Matteo Ricci(1583-1610)in promoting Sino-Western cultural exchange during his mission in late Ming China,focusing on the period from his arrival in 1583 until his death in 1610....This paper explores the pivotal role of Matteo Ricci(1583-1610)in promoting Sino-Western cultural exchange during his mission in late Ming China,focusing on the period from his arrival in 1583 until his death in 1610.Ricci’s unique approach of cultural accommodation,scientific knowledge dissemination,and religious dialogue positioned him as a bridge between two vastly different civilizations.This study analyzes Ricci’s methods of engagement with Chinese scholars,his introduction of Western science,and the impact of his religious and philosophical exchanges.Ricci’s strategy of adopting Chinese customs and intellectual traditions allowed him to foster trust and dialogue,making him one of the most successful missionaries in China.The paper further examines how Ricci’s translations of scientific works and his attempts to harmonize Christianity with Confucian values significantly influenced Chinese intellectual circles.By introducing advanced European knowledge in astronomy,mathematics,and geography,Ricci not only facilitated scientific exchange but also enhanced the Jesuits’reputation among Chinese scholars.Ricci’s enduring legacy is examined in the context of early global interactions,emphasizing his influence on subsequent Jesuit missions and the broader history of intercultural dialogue between East and West,highlighting the transformative power of empathy,respect,and intellectual curiosity in cross-cultural engagements.展开更多
文摘本文研究了在Bakry-Émery Ricci曲率条件下加权Laplace算子的Li-Yau梯度估计的问题,利用Bochner公式与加权Laplace公式以及极大值定理等处理Li-Yau梯度问题的方法,获得了加权Laplace在Bakry-Émery Ricci曲率有下界的条件下,热方程的正解u (x, t)的最优Li-Yau梯度估计。In this paper, the problem of Li-Yau gradient estimation of weighted Laplace operator under Bakry-Émery Ricci curvature is studied. Bochner formula, weighted Laplace formula and the maximum theorem are used to deal with the Li-Yau gradient problem. The optimal Li-Yau gradient estimation for the positive solution u (x, t) of the heat equation is obtained under the condition of lower bound for weighted Laplace Bakry-Émery Ricci curvature.
基金Supported by the National Natural Science Foundation of China(11771020,12171005).
文摘In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.
基金supported by the YSBR-001,the NSFC(12201597)research funds from USTC(University of Science and Technology of China)and CAS(Chinese Academy of Sciences)+2 种基金supported by the YSBR-001the NSFC(11971452,12026251)a research fund from USTC.
文摘This paper is the sequel to our study of heat kernel on Ricci shrinkers[29].In this paper,we improve many estimates in[29]and extend the recent progress of Bamler[2].In particular,we drop the compactness and curvature boundedness assumptions and show that the theory of F-convergence holds naturally on any Ricci flows induced by Ricci shrinkers.
文摘This paper explores the pivotal role of Matteo Ricci(1583-1610)in promoting Sino-Western cultural exchange during his mission in late Ming China,focusing on the period from his arrival in 1583 until his death in 1610.Ricci’s unique approach of cultural accommodation,scientific knowledge dissemination,and religious dialogue positioned him as a bridge between two vastly different civilizations.This study analyzes Ricci’s methods of engagement with Chinese scholars,his introduction of Western science,and the impact of his religious and philosophical exchanges.Ricci’s strategy of adopting Chinese customs and intellectual traditions allowed him to foster trust and dialogue,making him one of the most successful missionaries in China.The paper further examines how Ricci’s translations of scientific works and his attempts to harmonize Christianity with Confucian values significantly influenced Chinese intellectual circles.By introducing advanced European knowledge in astronomy,mathematics,and geography,Ricci not only facilitated scientific exchange but also enhanced the Jesuits’reputation among Chinese scholars.Ricci’s enduring legacy is examined in the context of early global interactions,emphasizing his influence on subsequent Jesuit missions and the broader history of intercultural dialogue between East and West,highlighting the transformative power of empathy,respect,and intellectual curiosity in cross-cultural engagements.
基金Supported by the National Natural Science Foundation of China(11371386)the European Union’s Seventh Framework Programme(FP7/2007-2013)under grant agreement(317721)
