In this paper,we study the Neumann boundary value problem of the Yang-Mills α-flow over a 4-dimensional compact Riemannian manifold with boundary.We establish the short-time existence of the Yang-Millsα-flow in the ...In this paper,we study the Neumann boundary value problem of the Yang-Mills α-flow over a 4-dimensional compact Riemannian manifold with boundary.We establish the short-time existence of the Yang-Millsα-flow in the framework of functional analysis and derive long-time existence and convergence results of classical solutions to the Yang-Millsα-flow,provided that theα-energy of initial connection is below some threshold.We also prove the validity of the boundary version of small energy estimates,removal of isolated singularities,and energy lower bound result for non-flat Yang-Mills connections.These results lead to the bubbling convergence of a sequence of Yang-Millsα-connections,and as an application,we demonstrate the existence of non-trivial Yang-Mills connections with Neumann boundary.展开更多
For a sequence of approximate Dirac-harmonic maps from a Riemannian surface with a smooth boundary into a stationary Lorentzian manifold, we study the boundary blow-up analysis and prove the positive energy identity f...For a sequence of approximate Dirac-harmonic maps from a Riemannian surface with a smooth boundary into a stationary Lorentzian manifold, we study the boundary blow-up analysis and prove the positive energy identity for spinors and the Lorentzian energy identity for maps. Moreover, the positive energy identity for maps holds when the target is a static Lorentzian manifold.展开更多
For a sequence of approximate Dirac-harmonic maps from a closed spin Riemann surface into a stationary Lorentzian manifold with uniformly bounded energy,we study the blow-up analysis and show that the Lorentzian energ...For a sequence of approximate Dirac-harmonic maps from a closed spin Riemann surface into a stationary Lorentzian manifold with uniformly bounded energy,we study the blow-up analysis and show that the Lorentzian energy identity holds.Moreover,when the targets are static Lorentzian manifolds,we prove the positive energy identity and the no neck property.展开更多
We consider the gauge transformations of a metricG-bundle over a compact Riemannian surface with boundary.By employing the heat flow method,the local existence and the long time existence of generalized solution are p...We consider the gauge transformations of a metricG-bundle over a compact Riemannian surface with boundary.By employing the heat flow method,the local existence and the long time existence of generalized solution are proved.展开更多
基金supported by the National Natural Science Foundation of China(12201515)the National Natural Science Foundation of China(12171314)+1 种基金partially supported by the Innovation Program of Shanghai Municipal Education Commission(2021-01-07-00-02-E00087)the Shanghai Frontier Science Center of Modern Analysis。
文摘In this paper,we study the Neumann boundary value problem of the Yang-Mills α-flow over a 4-dimensional compact Riemannian manifold with boundary.We establish the short-time existence of the Yang-Millsα-flow in the framework of functional analysis and derive long-time existence and convergence results of classical solutions to the Yang-Millsα-flow,provided that theα-energy of initial connection is below some threshold.We also prove the validity of the boundary version of small energy estimates,removal of isolated singularities,and energy lower bound result for non-flat Yang-Mills connections.These results lead to the bubbling convergence of a sequence of Yang-Millsα-connections,and as an application,we demonstrate the existence of non-trivial Yang-Mills connections with Neumann boundary.
基金supported by National Natural Science Foundation of China (Grant No. 12201515)the Natural Science Foundation of Chongqing, China (Grant No. cstc2021jcyj-msxmX1058)+4 种基金the China Scholarship Council (Grant No. 202206995009)supported by National Natural Science Foundation of China (Grant No. 12101255).supported by Innovation Program of Shanghai Municipal Education Commission (Grant No. 2021-01-07-00-02-E00087)National Natural Science Foundation of China (Grant No. 12171314)Shanghai Frontier Science Center of Modern Analysis。
文摘For a sequence of approximate Dirac-harmonic maps from a Riemannian surface with a smooth boundary into a stationary Lorentzian manifold, we study the boundary blow-up analysis and prove the positive energy identity for spinors and the Lorentzian energy identity for maps. Moreover, the positive energy identity for maps holds when the target is a static Lorentzian manifold.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.SWU119064)supported by Shanghai Frontier Research Institute for Modern Analysis(IMA-Shanghai)and Innovation Program of Shanghai Municipal Education Commission(Grant No.2021-01-07-00-02-E00087)。
文摘For a sequence of approximate Dirac-harmonic maps from a closed spin Riemann surface into a stationary Lorentzian manifold with uniformly bounded energy,we study the blow-up analysis and show that the Lorentzian energy identity holds.Moreover,when the targets are static Lorentzian manifolds,we prove the positive energy identity and the no neck property.
文摘We consider the gauge transformations of a metricG-bundle over a compact Riemannian surface with boundary.By employing the heat flow method,the local existence and the long time existence of generalized solution are proved.
