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	1. Rigidity of polyhedral surfaces with finite boundary components
	Ba Te,Zhou Ze
	Mathematics 08 April 2021
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	Abstract:We prove that the polyhedral surface with finite boundary components is determined up to isometry(or scaling) by some types of discrete curvatures, which generalizes a classical result of Luo Feng. The basic idea is to apply the doubling surgery. In this way, the rigidity of surface with boundary is a corollary of the rigidity of closed surface.
	TO cite this article:Ba Te,Zhou Ze. Rigidity of polyhedral surfaces with finite boundary components[OL].[ 8 April 2021] http://en.paper.edu.cn/en_releasepaper/content/4754475


	2. Notes on Vortex Filament Equation
	SONG Chong
	Mathematics 09 May 2016
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	Abstract:Vortex filament equation is one of the most important equations in classical theory of fluid dynamics. In this note, we study the properties of the evolution surface of the vortex filament and give the reduced forms of the vortex filament equation in different gauge.
	TO cite this article:SONG Chong. Notes on Vortex Filament Equation[OL].[ 9 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4687174

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	3. Gauss Map of Skew Mean Curvature Flow
	SONG Chong
	Mathematics 09 May 2016
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	Abstract:The Skew Mean Curvature Flow(SMCF) is a natural generalization of the famous Vortex Filament Equation in higher dimensions. In this note, we show that the Gauss map of the SMCF satisfies a sch flow equation.
	TO cite this article:SONG Chong. Gauss Map of Skew Mean Curvature Flow[OL].[ 9 May 2016] http://en.paper.edu.cn/en_releasepaper/content/4687177


	4. Hypersurfaces with Prescribed $lpha$-Relative Gauss-Kronecker Curvature
	WU Yadong,ZHAO Guosong
	Mathematics 25 December 2013
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	Abstract:Considering the $lpha$-relative normalizationon hypersurfaces, we derive the equations of hypersurfaces with$lpha$-relative Gauss-Kronecker curvature. By solving two linkedMonge-Amp$grave{e}$re equations with Dirichlet boundary conditions,we construct hyperbolic hypersurfaces such that their$lpha$-relative Gauss-Kronecker curvature are the given functions.
	TO cite this article:WU Yadong,ZHAO Guosong. Hypersurfaces with Prescribed $lpha$-Relative Gauss-Kronecker Curvature[OL].[25 December 2013] http://en.paper.edu.cn/en_releasepaper/content/4578330


	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. 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


	7. Conformal Isoparametric Hypersurfaces with Two Distinct Conformal Principal Curvatures in Conformal Space
	Nie Changxiong,Li TongZhu,HE YiJun,WU ChuanXi
	Mathematics 10 March 2010
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	Abstract:The conformal geometry of regular hypersurfaces in the conformal space is studied. We classify all the conformal isoparametric hypersurfaces with two distinct conformal principal curvatures in the conformal space up to conformal equivalence.
	TO cite this article:Nie Changxiong,Li TongZhu,HE YiJun, et al. Conformal Isoparametric Hypersurfaces with Two Distinct Conformal Principal Curvatures in Conformal Space[OL].[10 March 2010] http://en.paper.edu.cn/en_releasepaper/content/40560


	8. A Rigidity Theorem for Affine Kahler-Ricci Flat Graph
	An－Min Li,Ruiwei Xu
	Mathematics 12 January 2010
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	Abstract:A well-known theorem of Pogorelov states that any smooth strictly convex solution of Pogorelov\
	TO cite this article:An－Min Li,Ruiwei Xu. A Rigidity Theorem for Affine Kahler-Ricci Flat Graph[OL].[12 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38797


	9. Projective Blaschke manifolds
	An－Min Li,Guosong Zhao
	Mathematics 08 January 2010
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	Abstract:In this paper we define the concept of Projective Blaschke manifolds and extend the theory of equiaffine differential geometry to the projective Blaschke manifolds. We prved that if M be a complete projective Blaschke n-sphere and its universal covering manifold is isometric to a complete (n+1) dimensional parabolic, elliptic or hyperbolic affine hypersphere, then M is a quotient space of E^n, S^n or D^n by a isometric subgroup of its corresponding spaces.
	TO cite this article:An－Min Li,Guosong Zhao. Projective Blaschke manifolds[OL].[ 8 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38663


	10. Vortex equations on complete Hermitian manifolds
	Zhang Xi
	Mathematics 06 January 2010
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	Abstract:In this paper, we will investigate one type of vortex equations over various complete noncompact Hermitian manifolds, the related metric will be called Hermitian Yang-Mills-Higgs metric. Using the solvability of Dirichlet problem in [16] and compact exhaustion method, we can solve these Vortex equation on complete Hermitian manifold, under some conditions on the complete Hermitian manifold and the initial Hermitian metric. Then, we obtain a existence theorem of Hermitian Yang-Mills-Higgs metric on complete Hermitian manifold, this result can be seen as a generalization of the result about Hermitian Yang-Mills metrics in [22].
	TO cite this article:Zhang Xi. Vortex equations on complete Hermitian manifolds[OL].[ 6 January 2010] http://en.paper.edu.cn/en_releasepaper/content/38555

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