王嵬
博士 教授 博士生导师
北京大学 数学科学学院
辛几何与非线性分析
个性化签名
- 姓名:王嵬
- 目前身份:在职研究人员
- 担任导师情况:博士生导师
- 学位:博士
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学术头衔:
博士生导师
- 职称:高级-教授
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学科领域:
微分几何学
- 研究兴趣:辛几何与非线性分析
王嵬 北京大学数学科学学院 数学物理教研室 教授
教育经历
2002 南开大学 学士
2007 南开大学 博士
工作经历
2017- 北京大学数学科学学院 教授
2011-2017 北京大学数学科学学院 副教授
2009-2011 北京大学数学科学学院 助理教授
2007-2009 北京大学数学科学学院 博士后
科研项目
2013-2015 辛几何与非线性分析 优秀青年基金
2010-2014 辛几何与非线性分析 全国优秀博士论文专项基金
2009-2011 辛几何与微分几何 自然科学基金(青年基金)
2008-2010 辛几何与非线性分析 中国博士后科学基金(特别资助)
荣誉获奖
2009 全国优秀博士论文
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主页访问
115
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关注数
0
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成果阅读
684
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成果数
9
【期刊论文】Irrationally elliptic closed characteristics on compact convex hypersurfaces in
Journal of Functional Analysis,2014,267(3):799-841
2014年08月01日
In this paper, let be a compact convex hypersurface which carries exactly three geometrically distinct closed characteristics. We prove that at least two of them must be irrationally elliptic.
Compact convex hypersurfaces Closed characteristics Hamiltonian systems Morse theory
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【期刊论文】Resonance identities for closed characteristics on compact star-shaped hypersurfaces in
Journal of Functional Analysis,2014,266(9):5598-5638
2014年05月01日
Resonance relations among periodic orbits on given energy hypersurfaces are very important for getting deeper understanding of the dynamics of the corresponding Hamiltonian systems. In this paper, we establish two new resonance identities for closed characteristics on every compact star-shaped hypersurface Σ in when the number of geometrically distinct closed characteristics on Σ is finite, which extend those identities established by C. Viterbo in 1989 for star-shaped hypersurfaces assuming in addition that all the closed characteristics and their iterates are non-degenerate, and that by W. Wang, X. Hu and Y. Long in 2007 for strictly convex hypersurfaces in .
Compact star-shaped hypersurfaces Closed characteristics Hamiltonian systems Resonance identity
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【期刊论文】Stability of closed characteristics on symmetric compact convex hypersurfaces in
Journal de Mathématiques Pures et Appliquées,2013,99(3):297-308
2013年03月01日
In this article, let be a compact convex hypersurface which is symmetric with respect to the origin. We prove that if Σ carries finitely many geometrically distinct closed characteristics, then at least of them must be non-hyperbolic; if Σ carries exactly n geometrically distinct closed characteristics, then at least two of them must be elliptic.
Compact convex hypersurfaces Closed characteristics Hamiltonian systems Index iteration
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【期刊论文】On the average indices of closed geodesics on positively curved Finsler spheres
Mathematische Annalen,2012,355():1049–1065&
2012年04月11日
In this paper, we prove that on every Finsler n-sphere (S n, F) for n ≥ 6 with reversibility λ and flag curvature K satisfying (λλ+1)2<K≤1 , either there exist infinitely many prime closed geodesics or there exist [n2]−2 closed geodesics possessing irrational average indices. If in addition the metric is bumpy, then there exist n−3 closed geodesics possessing irrational average indices provided the number of prime closed geodesics is finite.
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【期刊论文】On a conjecture of Anosov
Advances in Mathematics,2012,230(4-6):1597-1617
2012年08月01日
In this paper, we prove that for every bumpy Finsler -sphere with reversibility and flag curvature satisfying , there exist prime closed geodesics. This gives a confirmed answer to a conjecture of Anosov [1] in 1974 for a generic case.
Finsler spheres Closed geodesics Index iteration Mean index identity,, stability
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104浏览
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【期刊论文】Stability of closed characteristics on compact convex hypersurfaces in $\R^6$
J. Eur. Math. Soc,-0001,():
-1年11月30日
In this paper, let $\Sigma\subset\R^{6}$ be a compact convex hypersurface. We prove that if Σ carries only finitely many geometrically distinct closed characteristics, then at least two of them must possess irrational mean indices. Moreover, if $\Sg$ carries exactly three geometrically distinct closed characteristics, then at least two of them must be elliptic.
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【期刊论文】Stability of closed geodesics on Finsler 2-spheres
Journal of Functional Analysis,2008,255(3):620-641
2008年08月01日
In this paper, we prove that on every Finsler 2-dimensional sphere, either there exist infinitely many prime closed geodesics or there exist at least two irrationally elliptic prime closed geodesics.
Finsler spheres Closed geodesics Index iteration Mean index identity Morse inequality Stability
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【期刊论文】Closed geodesics on positively curved Finsler spheres
Advances in Mathematics,2008,218(5):1566-1603
2008年08月01日
In this paper, we prove that for every Finsler n-sphere for with reversibility λ and flag curvature K satisfying , either there exist infinitely many prime closed geodesics or there exists one elliptic closed geodesic whose linearized Poincaré map has at least one eigenvalue which is of the form with an irrational μ. Furthermore, there always exist three prime closed geodesics on any satisfying the above pinching condition.
Finsler spheres Closed geodesics Index iteration Mean index identity Stability
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Duke Math. J,-0001,():
-1年11月30日
There is a long standing conjecture in Hamiltonian analysis which claims that there exist at least n geometrically distinct closed characteristics on every compact convex hypersurface in $\R^{2n}$ with n≥2. Besides many partial results, this conjecture has been only completely solved for n=2. In this paper, we give a confirmed answer to this conjecture for n=3. In order to prove this result, we establish first a new resonance identity for closed characteristics on every compact convex hypersurface $\Sg$ in $\R^{2n}$ when the number of geometrically distinct closed characteristics on $\Sg$ is finite. Then using this identity and earlier techniques of the index iteration theory, we prove the mentioned multiplicity result for $\R^6$. If there are exactly two geometrically distinct closed characteristics on a compact convex hypersuface in $\R^4$, we prove that both of them must be irrationally elliptic.
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