In this paper,we discuss a Kazdan-Warner typed equation on certain non-compact Rie- mannian manifolds.As an application,we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles o...In this paper,we discuss a Kazdan-Warner typed equation on certain non-compact Rie- mannian manifolds.As an application,we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles over certain non-compact K(?)hler manifolds.展开更多
Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous map.We assume that the dynamical system satisfies g-almost product property and the uniform separation property.We c...Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous map.We assume that the dynamical system satisfies g-almost product property and the uniform separation property.We compute the topological pressure of saturated sets under these two conditions.If the uniform separation property does not hold,we compute the topological pressure of the set of generic points.We give an application of these results to multifractal analysis and finally get a conditional variational principle.展开更多
In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilib... In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4].展开更多
Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.
Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying...Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying T ＊｜X = T and T ＊x＊ = x＊. We show that their topological entropies satisfy hd（T, X） ≥ h（T ＊, X＊） if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space.展开更多
基金the National Natural Science Foundation of China(Grant No.10771188)the Natural Science Foundation of Zhejiang Province(Grant No.Y605091)
文摘In this paper,we discuss a Kazdan-Warner typed equation on certain non-compact Rie- mannian manifolds.As an application,we prove an existence theorem of Hermitian-Yang-Mills-Higgs metrics on holomorphic line bundles over certain non-compact K(?)hler manifolds.
基金supported by National Natural Science Foundation of China (Grant No.10571086)the National Basic Research Program of China (Grant No.2007CB814800)
文摘Let (X,d,T) be a dynamical system,where (X,d) is a compact metric space and T:X → X is a continuous map.We assume that the dynamical system satisfies g-almost product property and the uniform separation property.We compute the topological pressure of saturated sets under these two conditions.If the uniform separation property does not hold,we compute the topological pressure of the set of generic points.We give an application of these results to multifractal analysis and finally get a conditional variational principle.
基金the National Natural Science Foundation of China (Grant No.10171043)
文摘 In this note we first prove a fixed point theorem in H-spaces which unities and extends the corresponding results in [6] and [9]. Then, by applying the fixed point theorem, we prove an existence theorem of an equilibrium point of an abstract economy in H-spaces which improves and generalizes similar result in [4].
文摘Let f : S → P 1 be a semistable family of curves of genus g 2. We prove that if f admits exactly 5 singular fibers and 4 of them have non-compact Jacobian, then g = 2.
基金supported by the Fundamental Research Funds for the Central Universities (CDJZR10100006)
文摘Let T ： X → X be a uniformly continuous homeomorphism on a non-compact metric space （X, d）. Denote by X＊ = X ∪ {x＊} the one point compactification of X and T ＊ ： X＊ → X＊ the homeomorphism on X＊ satisfying T ＊｜X = T and T ＊x＊ = x＊. We show that their topological entropies satisfy hd（T, X） ≥ h（T ＊, X＊） if X is locally compact. We also give a note on Katok’s measure theoretic entropy on a compact metric space.
