In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe ...In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.展开更多
A fundamental problem in four dimensional differential topology is to find a surface with minimal genus which represents a given homology class. This problem was considered by many people for closed 4 manifolds. In th...A fundamental problem in four dimensional differential topology is to find a surface with minimal genus which represents a given homology class. This problem was considered by many people for closed 4 manifolds. In this paper,we consider this problem for four manifold with boundary.展开更多
Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold...Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold. In this paper, the authors first show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M（dim M - 1）. Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.展开更多
We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behav...We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times.展开更多
基金Supported by National Natural Science Foundation of China under Grant No.10801027Fok Ying Tong Education Foundation under Grant No.121003
文摘In this paper,we define lower-dimensional volumes of spin manifolds with boundary.We compute thelower-dimensional volume Vol^((2,2)) for 5-dimensional and 6-dimensional spin manifolds with boundary and we also getthe Kastler-Kalau-Walze type theorem in this case.
文摘A fundamental problem in four dimensional differential topology is to find a surface with minimal genus which represents a given homology class. This problem was considered by many people for closed 4 manifolds. In this paper,we consider this problem for four manifold with boundary.
基金Project supported by the National Natural Science Foundation of China (Nos. 10601053, 10671096,10871184, 10971104)Beijing International Mathematical Research Center for the hospitality and financial support during the course of this work
文摘Seventy years ago, Myers and Steenrod showed that the isometry group of a Riemannian manifold without boundary has a structure of Lie group. In 2007, Bagaev and Zhukova proved the same result for a Riemannian orbifold. In this paper, the authors first show that the isometry group of a Riemannian manifold M with boundary has dimension at most 1/2 dim M（dim M - 1）. Then such Riemannian manifolds with boundary that their isometry groups attain the preceding maximal dimension are completely classified.
文摘We use reflecting Brownian motion(RBM)to prove the well-known Gauss–Bonnet–Chern theorem for a compact Riemannian manifold with boundary.The boundary integrand is obtained by carefully analyzing the asymptotic behavior of the boundary local time of RBM for small times.
