In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing ...In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.展开更多
In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the u...In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.展开更多
We investigate electron mesoscopic transport in a three-terminal setup with coupled quantum dots and a magnetic flux.By mapping the original transport problem into a non-Hermitian Hamiltonian form,we study the interpl...We investigate electron mesoscopic transport in a three-terminal setup with coupled quantum dots and a magnetic flux.By mapping the original transport problem into a non-Hermitian Hamiltonian form,we study the interplay between the coherent couplings between quantum dots,the magnetic flux,and the dissipation due to the tunnel coupling with the reservoirs.展开更多
基金Supported by the National Natural Science Foundation of China(11971450)partially supported by the Project of Stable Support for Youth Team in Basic Research Field,CAS(YSBR-001)。
文摘In this paper,we introduce and prove three analytic results related to uniform convergence,properties of Newtonian potential,and convergence of sequences in Sobolev space constrained by their Laplacian.Then,utilizing our analytic results,we develop a complete proof of a crucial estimate appearing in the results of Guofang Wang and Xiaohua Zhu,which states the classification of extremal Hermitian metrics with finite energy and area on compact Riemann surfaces and finite singularities satisfying small singular angles.
文摘In this article,we are concerned with the C^(2)estimates for the k-convex solutions of a class of degenerate k-Hessian equations on closed Hermitian manifolds,whose function in the right-hand side is relevant to the unknown function and its gradient.We will get C^(0)estimate by promoting others′results,and get the“HMW estimate”of this equation such that the conditions of using blow-up analysis are satisfied,and the gradient estimate and second-order estimate will be obtained.Such an estimate will be helpful to study the existence for the solution of the equation.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1404400)the National Natural Science Foundation of China(Grant No.12125504 and 12305050)+2 种基金Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ25A050001)the Hundred Talents Program of the Chinese Academy of Sciencesthe Natural Science Foundation of Jiangsu Higher Education Institutions of China(Grant No.23KJB140017)。
文摘We investigate electron mesoscopic transport in a three-terminal setup with coupled quantum dots and a magnetic flux.By mapping the original transport problem into a non-Hermitian Hamiltonian form,we study the interplay between the coherent couplings between quantum dots,the magnetic flux,and the dissipation due to the tunnel coupling with the reservoirs.
