Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. ...Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.展开更多
In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fu...In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.展开更多
A three-dimensional large eddy simulation （LES） of a spatially developing round jet is carried out in cylindrical coordinates using a dynamic subgrid model with strong inflow instability. Evolutions of large-scale v...A three-dimensional large eddy simulation （LES） of a spatially developing round jet is carried out in cylindrical coordinates using a dynamic subgrid model with strong inflow instability. Evolutions of large-scale vortex structures represented by tangential vortices are obtained and compared with flow visualization. Also presented are three-dimensional spatial evolutions of coherent structure, which are of quasi two-dimensional Kelvin-Helmholtz instability and vortex rings as well as breaking up of the vortex rings with fully three-dimensional characteristics. Predicted results of mean velocity and turbulent intensity agree well with experiments. They are also compared with the results predicted by LES using standard Smagorinsky model and show good self-similarity. Turbulence spectrum of the predicted velocity shows the -5/3 decay for higher wave number, as expected for turbulent round jet flows. In addition, fl-test and y-test are carded out for the instantaneous velocity, showing that the present LES method can successfully predict the hierarchical structure of round jet.展开更多
In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional .M2p of a submanifold Mn in a general Riemannian manifold gn^n＋m for p = 0, 1,.....In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional .M2p of a submanifold Mn in a general Riemannian manifold gn^n＋m for p = 0, 1,..., [n/2]. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional M2p, called relatively 2p-minimal submanifolds, for all p. At last, we discuss the relations between relatively 2p-minimal submanifoIds and austere submanifolds in real space forms, as well as a special variational problem.展开更多
For a compact Riemannian manifold NRK without boundary, we establish the existence of strong solutions to the heat flow for harmonic maps from Rn to N, and the regularizing rate estimate of the strong solutions. Moreo...For a compact Riemannian manifold NRK without boundary, we establish the existence of strong solutions to the heat flow for harmonic maps from Rn to N, and the regularizing rate estimate of the strong solutions. Moreover, we obtain the analyticity in spatial variables of the solutions. The uniqueness of the mild solutions in C([0,T]; W1,n) is also considered in this paper.展开更多
文摘Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.
文摘In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.
基金supported by the National Natural Science Foundation of China (Grant Nos. 50176027 and 50706021)a grant from the Research Committee of The Hong Kong Polytechnic University (Grant No.G-U294)
文摘A three-dimensional large eddy simulation （LES） of a spatially developing round jet is carried out in cylindrical coordinates using a dynamic subgrid model with strong inflow instability. Evolutions of large-scale vortex structures represented by tangential vortices are obtained and compared with flow visualization. Also presented are three-dimensional spatial evolutions of coherent structure, which are of quasi two-dimensional Kelvin-Helmholtz instability and vortex rings as well as breaking up of the vortex rings with fully three-dimensional characteristics. Predicted results of mean velocity and turbulent intensity agree well with experiments. They are also compared with the results predicted by LES using standard Smagorinsky model and show good self-similarity. Turbulence spectrum of the predicted velocity shows the -5/3 decay for higher wave number, as expected for turbulent round jet flows. In addition, fl-test and y-test are carded out for the instantaneous velocity, showing that the present LES method can successfully predict the hierarchical structure of round jet.
基金supported by National Natural Science Foundation of China(Grant No.11001016)the Specialized Research Fund for the Doctoral Program of Higher Education(Grant No. 20100003120003)the Program for Changjiang Scholars and Innovative Research Team in University
文摘In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional .M2p of a submanifold Mn in a general Riemannian manifold gn^n＋m for p = 0, 1,..., [n/2]. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the functional M2p, called relatively 2p-minimal submanifolds, for all p. At last, we discuss the relations between relatively 2p-minimal submanifoIds and austere submanifolds in real space forms, as well as a special variational problem.
基金supported by National Natural Science Foundation of China (GrantNos. 10701064, 10931001 and 11171061) Fundamental Research Funds for the Central Universities Program(Grant Nos. 2012QNA3008 and 12D10912)
文摘For a compact Riemannian manifold NRK without boundary, we establish the existence of strong solutions to the heat flow for harmonic maps from Rn to N, and the regularizing rate estimate of the strong solutions. Moreover, we obtain the analyticity in spatial variables of the solutions. The uniqueness of the mild solutions in C([0,T]; W1,n) is also considered in this paper.
