In this paper, Yau’s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite di...In this paper, Yau’s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional and strong Liouville theorem holds in Alexandrov spaces with nonnegative curvature.展开更多
An algorithm is given for computing in a very efficient way the topology of two real algebraic plane curves defined implicitly.The authors preform a symbolic pre-processing that allows us later to execute all numerica...An algorithm is given for computing in a very efficient way the topology of two real algebraic plane curves defined implicitly.The authors preform a symbolic pre-processing that allows us later to execute all numerical computations in an accurate way.展开更多
We prove that any abelian cover over a smooth variety is defined by some cyclic equations. From the defining equations, we compute explicitly the normalization, branch locus, ramification indices, global invariants, a...We prove that any abelian cover over a smooth variety is defined by some cyclic equations. From the defining equations, we compute explicitly the normalization, branch locus, ramification indices, global invariants, and the resolution of singularities. As an application, we construct a new algebraic surface which is the quotient of ball.展开更多
文摘In this paper, Yau’s conjecture on harmonic functions in Riemannian manifolds is generalized to Alexandrov spaces. It is proved that the space of harmonic functions with polynomial growth of a fixed rate is finite dimensional and strong Liouville theorem holds in Alexandrov spaces with nonnegative curvature.
文摘An algorithm is given for computing in a very efficient way the topology of two real algebraic plane curves defined implicitly.The authors preform a symbolic pre-processing that allows us later to execute all numerical computations in an accurate way.
基金supported by National Natural Science Foundation of China (Grant No.10731030)the Innovation Program of Shanghai Municipal Education Commission (Grant No. 11ZZ18)
文摘We prove that any abelian cover over a smooth variety is defined by some cyclic equations. From the defining equations, we compute explicitly the normalization, branch locus, ramification indices, global invariants, and the resolution of singularities. As an application, we construct a new algebraic surface which is the quotient of ball.
