共查询到19条相似文献,搜索用时 78 毫秒
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研究Riemann流形的球面特征是一个颇有兴趣的问题,特别是考虑完备Riemann流形M在什么条件下与一球面等距.为此,Obata曾得到两个微分方程组,证明它们在M上非常数解的存在性等价于M与一个球面等距,其中一个方程组解的存在与共形向量场的存在有关.人们由此给出M在紧致情况下很多解的存在条件(如[3]).而另一个是下面的(也见[4]).定理A设M为n维完备、连通、单连通的Riemann流形,则下列微分方程组 相似文献
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考察了从Riemann流形M到完备Riemann流形N的驻点调和映射 ,证明了其奇异集包含在Q1∪Q3 中 相似文献
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设M为完备非紧的黎曼流形,本文在M×[0,+∞)上得到了如下一类含负指数项抛物型方程的正解的梯度估计:u=t=△u+cu~(-α),其中α0和c为两个固定常数.这一结果推广了杨云雁教授关于流形上含负指数项椭圆型方程梯度估计的结论[Acta Math.Sin.,Engl.Ser.,2010,26(6):1177-1182].同时这一结果也可以看作是对李嘉禹教授关于流形上含非线性项椭圆与抛物型方程梯度估计[J.Funct.Anal.,1991,100(2):153-201]的一个补充. 相似文献
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This paper considers the existence problem of an elliptic equation.which is equivalent to the prescribing conformal Gaussian curvature problem on R2.An existence result is pried.In particular,K(x)is allowed to be unbounded above. 相似文献
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Seongtag Kim 《Geometriae Dedicata》1997,64(3):373-381
We let (M,g) be a noncompact complete Riemannian manifold of dimension n 3 whose scalar curvature S(x) is positive for all x in M. With an assumption on the Ricci curvature and scalar curvature at infinity, we study the behavior of solutions of the Yamabe equation on –u+[(n–2)/(4(n–1))]Su=qu
(n+2)/(n–2) on (M,g). This study finds restrictions on the existence of an injective conformal immersion of (M,g) into any compact Riemannian n -manifold. We also show the existence of a complete conformal metric with constant positive scalar curvature on (M,g) with some conditions at infinity. 相似文献
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In this paper we consider the existence problem for the elliptic equation on , which arises in the study of conformal deformation of the hyperbolic disc. We prove an existence result for the above equation.
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张宗劳 《数学物理学报(A辑)》2002,22(1):135-144
设M是一个度量g的完备非紧非正曲率单连通黎曼流形,k是它的数曲率,K是M上的光滑函数.作者给出了M上以K作为数曲率且共形于g的度量的存在性条件,并给出了方程△u-hu+fu^p=0的一些正解存在性结果. 相似文献
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WU San-xing 《数学季刊》2006,(1)
This paper considers the existence problem of an elliptic equation, which is equivalent to solving the so called prescribing conformal Gaussian curvature problem on the hyperbolic disc H2. An existence result is proved. In particular, K(x) is allowed to be unbounded above. 相似文献
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本文我们得到了黎曼流形上一类非线性抛物方程的局部Hamilton梯度估计. 利用这个局部估计,我们得到了一个Harnack型不等式和一个Liouville型定理. 相似文献
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Consider a hypermanifold M
0 of a Riemannian manifold N whose Riccicurvature is bounded from below. If M
0 is transversal to a conformalvector field on N, then conditions are given, such that the meancurvature evolution of M
0 with Dirichlet boundary conditions has asolution for all times. 相似文献
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We suggest a new approach to the statement of boundary value problems for elliptic partial differential equations on arbitrary Riemannian manifolds which is based on the consideration of equivalence classes of functions on a manifold. Using this approach, we establish some interrelation between the solvability of boundary value problems and solvability of exterior boundary problems for the stationary Schrodinger equation. Also we prove the comparison and uniqueness theorems for solutions to boundary value problems in this statement and obtain sufficient conditions for solvability of boundary value problems when the coefficient in the Schrodinger equation is changed. 相似文献