In this paper,we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1 which,as Riemannian manifolds,are locally isometric to the Riemannian product of two Riemannian manifolds both pos...In this paper,we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1 which,as Riemannian manifolds,are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvature.As the main result,a complete classification of such affine hyperspheres is established.Moreover,as direct consequences,3-and 4-dimensional affine hyperspheres with parallel Ricci tensor are also classified.展开更多
We perform the analysis of the hp finite element approximation for the solution to singularly perturbed transmission problems, using Spectral Boundary Layer Meshes. In [12] it was shown that this method yields robust ...We perform the analysis of the hp finite element approximation for the solution to singularly perturbed transmission problems, using Spectral Boundary Layer Meshes. In [12] it was shown that this method yields robust exponential convergence, as the degree p of the approximating polynomials is increased, when the error is measured in the energy norm associated with the boundary value problem. In the present article we sharpen the result by showing that the hp-Finite Element Method （FEM） on Spectral Boundary Layer Meshes leads to robust exponential convergence in a stronger, more balanced norm. Several numerical results illustrating and extending the theory are also nresented.展开更多
We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures.In particular,we define local angl...We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures.In particular,we define local angle functions encoding the geometry of the Lagrangian submanifold at hand.We prove that these functions are constant in the special case that the Lagrangian immersion is the Gauss map of an isoparametric hypersurface of a sphere and give the relation with the constant principal curvatures of the hypersurface.We also use our techniques to classify all minimal Lagrangian submanifolds of the complex hyperquadric which have constant sectional curvatures and all minimal Lagrangian submanifolds for which all local angle functions,respectively all but one,coincide.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11771404)。
文摘In this paper,we study locally strongly convex affine hyperspheres in the unimodular affine space Rn+1 which,as Riemannian manifolds,are locally isometric to the Riemannian product of two Riemannian manifolds both possessing constant sectional curvature.As the main result,a complete classification of such affine hyperspheres is established.Moreover,as direct consequences,3-and 4-dimensional affine hyperspheres with parallel Ricci tensor are also classified.
文摘We perform the analysis of the hp finite element approximation for the solution to singularly perturbed transmission problems, using Spectral Boundary Layer Meshes. In [12] it was shown that this method yields robust exponential convergence, as the degree p of the approximating polynomials is increased, when the error is measured in the energy norm associated with the boundary value problem. In the present article we sharpen the result by showing that the hp-Finite Element Method （FEM） on Spectral Boundary Layer Meshes leads to robust exponential convergence in a stronger, more balanced norm. Several numerical results illustrating and extending the theory are also nresented.
基金supported by the Tsinghua University-KU Leuven Bilateral Scientific Cooperation Fundcollaboration project funded by National Natural Science Foundation of China+6 种基金supported by National Natural Science Foundation of China(Grant Nos.11831005 and 11671224)supported byNational Natural Science Foundation of China(Grant Nos.11831005 and 11671223)supported by National Natural Science Foundation of China(Grant No.11571185)the Research Foundation Flanders(Grant No.11961131001)supported by the Excellence of Science Project of the Belgian Government(Grant No.GOH4518N)supported by the KU Leuven Research Fund(Grant No.3E160361)the Fundamental Research Funds for the Central Universities。
文摘We introduce a structural approach to study Lagrangian submanifolds of the complex hyperquadric in arbitrary dimension by using its family of non-integrable almost product structures.In particular,we define local angle functions encoding the geometry of the Lagrangian submanifold at hand.We prove that these functions are constant in the special case that the Lagrangian immersion is the Gauss map of an isoparametric hypersurface of a sphere and give the relation with the constant principal curvatures of the hypersurface.We also use our techniques to classify all minimal Lagrangian submanifolds of the complex hyperquadric which have constant sectional curvatures and all minimal Lagrangian submanifolds for which all local angle functions,respectively all but one,coincide.
