A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an n-simplex and P（m） an m-gon. This paper gives formulas for ...A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an n-simplex and P（m） an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space △^n1 × △^n2 × P（m）, where n1 is odd.展开更多
The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula...The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We also prove that a smooth selfshrinker with low entropy is a hyperplane.展开更多
基金supported by the National Natural Science Foundation of China(No.11371118)the Specialized Research Fund for the Doctoral Program of Higher Education(No.20121303110004)the Natural Science Foundation of Hebei Province(No.A2011205075)
文摘A small cover is a closed manifold M^n with a locally standard （Z2）^n-action such that its orbit space is a simple convex polytope P^n. Let A^n denote an n-simplex and P（m） an m-gon. This paper gives formulas for calculating the number of D-J equivalent classes and equivariant homeomorphism classes of orientable small covers over the product space △^n1 × △^n2 × P（m）, where n1 is odd.
文摘The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We also prove that a smooth selfshrinker with low entropy is a hyperplane.
