This paper proves that any rotationally symmetric translating soliton of mean curvature flow in R3 is strictly convex if it is not a plane and it intersects its symmetric axis at one point. The authors also study the ...This paper proves that any rotationally symmetric translating soliton of mean curvature flow in R3 is strictly convex if it is not a plane and it intersects its symmetric axis at one point. The authors also study the symmetry of any translating soliton of mean curvature flow in Rn.展开更多
We study the ordinary differential equations related to rotationally symmetric pseudo-Khler metricsof constant scalar curvatures. We present various solutions on various holomorphic line bundles over projectivespaces ...We study the ordinary differential equations related to rotationally symmetric pseudo-Khler metricsof constant scalar curvatures. We present various solutions on various holomorphic line bundles over projectivespaces and their disc bundles, and discuss the phase change phenomenon when one suitably changes initialvalues.展开更多
In this paper,the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied.It is proved that the flow converges to a unique geodesi...In this paper,the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied.It is proved that the flow converges to a unique geodesic sphere,i.e.,every principle curvature of the hypersurfaces converges to a same constant under the flow.展开更多
We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder...We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.展开更多
The catenary shells of revolution are widely used in church constructions due to their unique mechanics'features.To have a better understanding of the deformation and stress of the catenary shells of revolution,we...The catenary shells of revolution are widely used in church constructions due to their unique mechanics'features.To have a better understanding of the deformation and stress of the catenary shells of revolution,we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations.Numerical simulations are carried out based on both Reissner-Meissner(R-M)mixed formulations and displacement formulations.Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter c,and reveal that the mechanics of the catenary shells of revolution has some advantages over the spherical shell for some loadings.Two complete codes in Maple are provided.展开更多
基金Project supported by the 973 Project of the Ministry of Science and Technology of China and the Trans-Century Training Programme Foundation for the Talents by the Ministry of Education of China.
文摘This paper proves that any rotationally symmetric translating soliton of mean curvature flow in R3 is strictly convex if it is not a plane and it intersects its symmetric axis at one point. The authors also study the symmetry of any translating soliton of mean curvature flow in Rn.
基金supported by National Natural Science Foundation of China (Grant Nos.10425101, 10631050)National Basic Research Program of China (973 Project) (Grant No. 2006cB805905)
文摘We study the ordinary differential equations related to rotationally symmetric pseudo-Khler metricsof constant scalar curvatures. We present various solutions on various holomorphic line bundles over projectivespaces and their disc bundles, and discuss the phase change phenomenon when one suitably changes initialvalues.
文摘In this paper,the motion of inverse mean curvature flow which starts from a closed star-sharped hypersurface in special rotationally symmetric spaces is studied.It is proved that the flow converges to a unique geodesic sphere,i.e.,every principle curvature of the hypersurfaces converges to a same constant under the flow.
文摘We consider the area-preserving mean curvature flow with free Neumann boundaries. We show that a rotationally symmetric n-dimensional hypersurface in R^(n+1)between two parallel hyperplanes will converge to a cylinder with the same area under this flow. We use the geometric properties and the maximal principle to obtain gradient and curvature estimates, leading to long-time existence of the flow and convergence to a constant mean curvature surface.
基金supported by Xi'an University of Architecture and Technology(Grant No.002/2040221134).
文摘The catenary shells of revolution are widely used in church constructions due to their unique mechanics'features.To have a better understanding of the deformation and stress of the catenary shells of revolution,we formulate the principal radii for two kinds of catenary shells of revolution and their displacement type governing equations.Numerical simulations are carried out based on both Reissner-Meissner(R-M)mixed formulations and displacement formulations.Our investigations show that both deformation and stress response of elastic catenary shells of revolution are sensitive to its geometric parameter c,and reveal that the mechanics of the catenary shells of revolution has some advantages over the spherical shell for some loadings.Two complete codes in Maple are provided.
