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1. Cappell-Miller analytic torsion on contact manifolds | |||
SU Guangxiang | |||
Mathematics 11 December 2013 | |||
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Abstract:Analytic torsion is an important invariant in global analysis. Complex-valued analytic torsion has been studied in recent years. In this paper, we define the Cappell-Miller analytic torsion of the contact complex on contact manifolds. We also get the anomaly formula of the Cappell-Miller analytic torsion in this case. | |||
TO cite this article:SU Guangxiang. Cappell-Miller analytic torsion on contact manifolds[OL].[11 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4574201 |
2. On some ratios of ergodic sums in continued fractions | |||
LIAO Lingmin | |||
Mathematics 26 February 2013 | |||
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Abstract:This note is devoted to the multifractal analysis of ratios of ergodic sums for Gauss dynamics T associated to continued fractions.For any irrational number x∈[0,1), let x=[a1(x),a2(x),...] be its continued fraction expansion with an(x)=a1(Tn-1x)being the partial quotients of x. The dimensions of the level sets defined by the ratios of the ergodic sums of a1(x) and a1(Tx)under the system ([0,1], T) and its iteration ([0,1], T2)are obtained.It will be seen that there are some differences between the cases here and the known multifratal analysis. | |||
TO cite this article:LIAO Lingmin. On some ratios of ergodic sums in continued fractions[OL].[26 February 2013] http://en.paper.edu.cn/en_releasepaper/content/4521387 |
3. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II | |||
Xie Qihong | |||
Mathematics 13 December 2012 | |||
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Abstract:A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W2(k). In this paper, first the author proves that smooth toric varieties are strongly liftable, hence the Kawamata-Viehweg vanishing theorem holds for smooth projective toric varieties. Second, the author proves the Kawamata-Viehweg vanishing theorem for normal projective surfaces which are birational to a strongly liftable smooth projective surface. Finally, the author deduces the cyclic cover trick over W2(k), which can be used to construct a large class ofliftable smooth projective varieties. | |||
TO cite this article:Xie Qihong. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic II[OL].[13 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503779 |
4. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic I | |||
Xie Qihong | |||
Mathematics 13 December 2012 | |||
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Abstract:A smooth scheme X over a field k of positive characteristic is said to be strongly liftable, if X and all prime divisors on X can be lifted simultaneously over W2(k). Some concrete examples and properties of strongly liftable schemes are given in this paper. As an application, the author proves that theKawamata-Viehweg vanishing theorem in positive characteristic holds on any normal projective surface which is birational to a strongly liftable surface. | |||
TO cite this article:Xie Qihong. Strongly Liftable Schemes and the Kawamata-Viehweg Vanishing in Positive Characteristic I[OL].[13 December 2012] http://en.paper.edu.cn/en_releasepaper/content/4503770 |
5. Gradient Estimates and Liouville Theorems for Dirac-harmonic maps | |||
CHEN Qun, Jürgen Jost,SUN Linlin | |||
Mathematics 07 August 2012 | |||
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Abstract:Dirac-harmonic map is the mathematical version of the super-symmetric nonlinear sigma model in quantum field theory, it includes the two important special cases: harmonic map and harmonic spinor. Many progresses have been made in the existence, regularity, blowup analysis, etc.. Most of the previous results deal with Dirac-harmonic maps from compact manifolds, it is the main aim of the present paper to derive properties of Dirac-harmonic maps from non-compact complete manifolds. Precisely, the authors established gradient estimates for Dirac-harmonic maps from non-compact complete Riemannian spin manifolds into regular balls of the target manifolds, and then apply these estimates to obtain Liouville theorems for Dirac-harmonic maps under certain conditions of the curvatures or energies, especially, they proved Liouville theorems of Dirac-harmonic maps under small energy density conditions. | |||
TO cite this article:CHEN Qun, Jürgen Jost,SUN Linlin. Gradient Estimates and Liouville Theorems for Dirac-harmonic maps[OL].[ 7 August 2012] http://en.paper.edu.cn/en_releasepaper/content/4486492 |
6. Finiteness theorems for equifocal hypersurfaces | |||
GE Jian-Quan, QIAN Chao, TANG Zi-Zhou | |||
Mathematics 31 December 2011 | |||
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Abstract:In this paper, we give a finiteness result on the diffeomorphismtypes of curvature-adapted equifocal hypersurfaces in a simply connected compact symmetric space. Furthermore, the condition curvature-adapted can be dropped if the symmetric space is of rank one. | |||
TO cite this article:GE Jian-Quan, QIAN Chao, TANG Zi-Zhou. Finiteness theorems for equifocal hypersurfaces[OL].[31 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4459008 |
7. Deforming symplectomorphism of certain irreducible Hermitiansymmetric spaces of compact type by mean curvature flow | |||
Lu Guangcun,Xiao Bang | |||
Mathematics 05 December 2011 | |||
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Abstract:In this paper, we generalize Medos-Wang‘s arguments andresults on the mean curvature flow deformations ofsymplectomorphisms of the complex projective spaces in Medos Wang[1]to a class of irreducible Hermitian symmetric spaces of compact typeincluding complex Grassmann manifolds and their compact totallygeodesic Kahler-Einstein submanifolds. | |||
TO cite this article:Lu Guangcun,Xiao Bang. Deforming symplectomorphism of certain irreducible Hermitiansymmetric spaces of compact type by mean curvature flow[OL].[ 5 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4453814 |
8. Deformations of special Legendrian submanifolds with boundary | |||
Lu Guangcun,Chen Xiaomin | |||
Mathematics 05 December 2011 | |||
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Abstract:In this article, for a compact special Legendrian submanifold withboundary of contact Calabi-Yau manifolds we study the deformationof it with boundary confined in an appropriately chosen contactsubmanifold of codimension two which we also call a scafford(Definition 4) by analogy with Butsher[1].Our result shows that it cannot bedeformed under such a boundary confinement. This result may be viewedas supplements of the compact boundless case considered by Tomassini andVezzoni[2]. | |||
TO cite this article:Lu Guangcun,Chen Xiaomin. Deformations of special Legendrian submanifolds with boundary[OL].[ 5 December 2011] http://en.paper.edu.cn/en_releasepaper/content/4453811 |
9. Variational formulas of higher order mean curvatures | |||
XU Ling,GE Jianquan | |||
Mathematics 01 November 2011 | |||
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Abstract:In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total 2p-th mean curvature functional of a n-dimensional submanifold M in a general (n+m)-dimensional Riemannian manifold N. As an example, we prove that closed complex submanifolds in complex projective spaces are critical points of the total 2p-th mean curvature functional, called relatively 2p-minimal submanifolds, for all p. At last, we discuss the relations between relatively 2p-minimal submanifolds and austere submanifolds in real space forms, as well as a special variational problem. | |||
TO cite this article:XU Ling,GE Jianquan. Variational formulas of higher order mean curvatures[OL].[ 1 November 2011] http://en.paper.edu.cn/en_releasepaper/content/4448166 |
10. S-λ Bases and S-λ Curves | |||
Fan Feilong ,Zeng Xiaoming | |||
Mathematics 23 May 2011 | |||
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Abstract:In this paper the S-λ distributions are presented and the S-λ basis functions are constructed from the S-λ distributions by means of the technique of generating functions and transform factors. These basis functions generate S-λ curves. We show that S-λ curves include Bezier curves, Poisson curves, rational Bezier curves and a lot of other curves. Therefore the researches of this paper provide a unified scheme for dealing with these famous curves. We study the important properties and identities of the S-λ basis functions and S-λ curves. Furthermore, by means of the technique of the generating function, a new convenient and practical method for local changes of S-λ curves is proposed. | |||
TO cite this article:Fan Feilong ,Zeng Xiaoming . S-λ Bases and S-λ Curves [OL].[23 May 2011] http://en.paper.edu.cn/en_releasepaper/content/4428911 |
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