In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strateg...In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.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
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
In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more...In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more complicated than what they have thought.We shall also give some detail calculations and found that our results fit quite well with earlier papers of the first author,one of them with X.X.Chen.展开更多
We propose a newmethod to generate surface quadrilateralmesh by calculating a globally defined parameterization with feature constraints.In the field of quadrilateral generation with features,the cross field methods a...We propose a newmethod to generate surface quadrilateralmesh by calculating a globally defined parameterization with feature constraints.In the field of quadrilateral generation with features,the cross field methods are wellknown because of their superior performance in feature preservation.The methods based on metrics are popular due to their sound theoretical basis,especially the Ricci flow algorithm.The cross field methods’major part,the Poisson equation,is challenging to solve in three dimensions directly.When it comes to cases with a large number of elements,the computational costs are expensive while the methods based on metrics are on the contrary.In addition,an appropriate initial value plays a positive role in the solution of the Poisson equation,and this initial value can be obtained from the Ricci flow algorithm.So we combine the methods based on metric with the cross field methods.We use the discrete dynamic Ricci flow algorithm to generate an initial value for the Poisson equation,which speeds up the solution of the equation and ensures the convergence of the computation.Numerical experiments show that our method is effective in generating a quadrilateral mesh for models with features,and the quality of the quadrilateral mesh is reliable.展开更多
Guided by the ternary leadership theory from the perspective of social psychology,this paper explores the impacts of authoritarian,benevolent,and moral leadership on the top design of the Grand Canal of China in terms...Guided by the ternary leadership theory from the perspective of social psychology,this paper explores the impacts of authoritarian,benevolent,and moral leadership on the top design of the Grand Canal of China in terms of its water management practice,while providing reference for resolving the“Matteo Ricci Puzzle”.The research findings are threefold:first,authoritarian as it is,the central government of China formulates relevant laws and regulations to provide legal system insurance for the construction of the Grand Canal Cultural Belt,thus providing the blueprint for constructing the“bright cultural belt,green ecological belt and colorful tourism belt of the Grand Canal”.Second,led by the Central Government,sticking to benevolent and moral leadership,China advocates scientific water management concepts and methods,and gives long-term and comprehensive care to the well-being of the people along the banks of the Grand Canal.Finally,the top-level design of the Grand Canal of China is based on the ternary leadership theory rooted in social psychology and has formulated a set of properly-scheduled,reasonably-coordinated,and flexibly-operated management system for the fundamental interests of the people and long-term goals of the country.展开更多
文摘In this article,we study Kahler metrics on a certain line bundle over some compact Kahler manifolds to find complete Kahler metrics with positive holomorphic sectional(or bisectional)curvatures.Thus,we apply a strategy to a famous Yau conjecture with a co-homogeneity one geometry.
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.
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 National Natural Science Foundation of China(Grant No.12171140).
文摘In this paper,we revisit the Kahler structures on the affine quadrics M1={z_(1)^(2)+z_(2)^(2)+z_(3)^(2)=1}in the paper by Bo Yang and Fang-Yang Zheng.We found that the Kahler structures on the complex surface are more complicated than what they have thought.We shall also give some detail calculations and found that our results fit quite well with earlier papers of the first author,one of them with X.X.Chen.
基金supported by NSFC Nos.61907005,61720106005,61936002,62272080.
文摘We propose a newmethod to generate surface quadrilateralmesh by calculating a globally defined parameterization with feature constraints.In the field of quadrilateral generation with features,the cross field methods are wellknown because of their superior performance in feature preservation.The methods based on metrics are popular due to their sound theoretical basis,especially the Ricci flow algorithm.The cross field methods’major part,the Poisson equation,is challenging to solve in three dimensions directly.When it comes to cases with a large number of elements,the computational costs are expensive while the methods based on metrics are on the contrary.In addition,an appropriate initial value plays a positive role in the solution of the Poisson equation,and this initial value can be obtained from the Ricci flow algorithm.So we combine the methods based on metric with the cross field methods.We use the discrete dynamic Ricci flow algorithm to generate an initial value for the Poisson equation,which speeds up the solution of the equation and ensures the convergence of the computation.Numerical experiments show that our method is effective in generating a quadrilateral mesh for models with features,and the quality of the quadrilateral mesh is reliable.
基金the research funding from the National Planning Office of Philosophy and Social Science Grant of P.R.China(18BGJ086).
文摘Guided by the ternary leadership theory from the perspective of social psychology,this paper explores the impacts of authoritarian,benevolent,and moral leadership on the top design of the Grand Canal of China in terms of its water management practice,while providing reference for resolving the“Matteo Ricci Puzzle”.The research findings are threefold:first,authoritarian as it is,the central government of China formulates relevant laws and regulations to provide legal system insurance for the construction of the Grand Canal Cultural Belt,thus providing the blueprint for constructing the“bright cultural belt,green ecological belt and colorful tourism belt of the Grand Canal”.Second,led by the Central Government,sticking to benevolent and moral leadership,China advocates scientific water management concepts and methods,and gives long-term and comprehensive care to the well-being of the people along the banks of the Grand Canal.Finally,the top-level design of the Grand Canal of China is based on the ternary leadership theory rooted in social psychology and has formulated a set of properly-scheduled,reasonably-coordinated,and flexibly-operated management system for the fundamental interests of the people and long-term goals of the country.
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)
