共查询到19条相似文献,搜索用时 109 毫秒
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严荣沐 《数学物理学报(A辑)》2004,24(4):420-425
该文对Finsler流形上的微分式定义了整体内积,进而引入δ算子和Laplace算子。该文还给出了δ算子的局部坐标表达式并且证明了Laplace算子可以看成是Riemann流形上Laplace算子在Finsler流形上的扩张。 相似文献
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本文首先推广了Capogna,Danielli和Garofalo关于p-次Laplace算子的径向解的一个重要公式,然后通过改进欧氏空间中证明Laplace算子的Hopf引理的方法,证明了H型群上p-次Laplace算子的Hopf型引理,进而证明了一个强极大值原理。 相似文献
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讨论了紧致无边流形上Laplace算子的特征值在Yamabe流上随时间的变化情况,结合极值原理得到了Laplace算子特征值的单调性. 相似文献
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本文给出了强Kaehler-Finsler流形上中值Laplace算子的一些性质,如自伴性质,散度形式等。与Kaehler流形上利用逆变基本张量及其在Finsler流形上的变形作为密度函数定义流形上的逐点内积及整体内积不同,作者利用强Kaehler-Finsler流形上的逆变密切Kaehler度量作为密度函数定义了流形上的逐点内积和整体内积,并定义了强Kaehler-Finsler流形上的Hodge-Laplace算子,它可看作函数情形中值Laplace算子的推广。 相似文献
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本文研究了黎曼流形上Laplace算子的第一特征值,利用流形的测地球上的Sobolev常数进行讨论并进行Moser迭代,得到闭的黎曼流形上Laplace算子第一特征值的一个下界估计. 相似文献
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本文证明了Heisenberg群上Laplace算子的Dirichlet特征值的存在性,给出了特征值的估计 相似文献
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在Finsler空间中给出了一种非线性的Laplace算子Δ,得到了Laplace算子Δ满足的性质,同时指出了Δ与Riemann空间中Laplace算子的异同. 相似文献
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A Hopf bundle, whose base manifold is the ring surface T2 and whose fiber is the group U(1), is established in this paper. On this Hopf bundle, the lifting of the Laplace operator on the base manifold is proved to be the Laplace operator on the Hopf bundle. The solutions of covariant derivative equations of cross section in associated bundles and the index theorem on the ring surface are also discussed. 相似文献
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Wolf Strübing 《manuscripta mathematica》1984,49(2):177-194
Integral formulas of Minkowski type, involving the higher mean curvatures as multilinear forms on the normal bundle, are proved for compact oriented immersed submanifolds with arbitrary codimension in a Riemannian manifold of constant curvature, and as application a generalization of the Liebmann-Süss theorem as well as upper bounds for the first positive eigenvalue of the Laplace operator are given. 相似文献
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Wolfgang Carl 《Foundations of Computational Mathematics》2016,16(5):1115-1150
This paper studies a Laplace operator on semi-discrete surfaces. A semi-discrete surface is represented by a mapping into three-dimensional Euclidean space possessing one discrete variable and one continuous variable. It can be seen as a limit case of a quadrilateral mesh, or as a semi-discretization of a smooth surface. Laplace operators on both smooth and discrete surfaces have been an object of interest for a long time, also from the viewpoint of applications. There are a wealth of geometric objects available immediately once a Laplacian is defined, e.g., the mean curvature normal. We define our semi-discrete Laplace operator to be the limit of a discrete Laplacian on a quadrilateral mesh, which converges to the semi-discrete surface. The main result of this paper is that this limit exists under very mild regularity assumptions. Moreover, we show that the semi-discrete Laplace operator inherits several important properties from its discrete counterpart, like symmetry, positive semi-definiteness, and linear precision. We also prove consistency of the semi-discrete Laplacian, meaning that it converges pointwise to the Laplace–Beltrami operator, when the semi-discrete surface converges to a smooth one. This result particularly implies consistency of the corresponding discrete scheme. 相似文献
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Chin-Yu Hsiao 《偏微分方程通讯》2017,42(6):895-942
Let M be an arbitrary complex manifold and let L be a Hermitian holomorphic line bundle over M. We introduce the Berezin–Toeplitz quantization of the open set of M where the curvature on L is nondegenerate. In particular, we quantize any manifold admitting a positive line bundle. The quantum spaces are the spectral spaces corresponding to [0,k?N], where N>1 is fixed, of the Kodaira Laplace operator acting on forms with values in tensor powers Lk. We establish the asymptotic expansion of associated Toeplitz operators and their composition in the semiclassical limit k→∞ and we define the corresponding star-product. If the Kodaira Laplace operator has a certain spectral gap this method yields quantization by means of harmonic forms. As applications, we obtain the Berezin–Toeplitz quantization for semi-positive and big line bundles. 相似文献
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《Nonlinear Analysis: Real World Applications》2008,9(5):2175-2184
In this paper, using the method of fibre bundle, we solve the coefficient problem in the operator of prolongation group with the aid of the conception of prolongation group for Lie transformation group. We obtain the permitted group of the vacuum Einstein equation, and introduce a doable program of getting local invariable solution of the equation. 相似文献
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Fabricio Macià 《偏微分方程通讯》2013,38(6):1137-1146
We study the concentration of eigenfunctions of the Laplace–Beltrami operator on manifolds all whose geodesics are closed (the so-called Zoll manifolds). Some results on the structure of the set of invariant semiclassical measures associated to sequences of eigenfunctions are given. Among these, we show that any probability measure on the unit tangent bundle of a compact rank-one symmetric space that is invariant by the geodesic flow may be realized as the semiclassical measure of a sequence of eigenfunctions of the Laplacian. This extends a previous result of Jakobson and Zelditch on spheres. 相似文献
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We provide operator-norm convergence estimates for solutions to a time-dependent equation of fractional elasticity in one spatial dimension, with rapidly oscillating coefficients that represent the material properties of a viscoelastic composite medium. Assuming periodicity in the coefficients, we prove operator-norm convergence estimates for an operator fibre decomposition obtained by applying to the original fractional elasticity problem the Fourier–Laplace transform in time and Gelfand transform in space. We obtain estimates on each fibre that are uniform in the quasimomentum of the decomposition and in the period of oscillations of the coefficients as well as quadratic with respect to the spectral variable. On the basis of these uniform estimates we derive operator-norm-type convergence estimates for the original fractional elasticity problem, for a class of sufficiently smooth densities of applied forces. 相似文献
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Ramzi Alsaedi 《复变函数与椭圆型方程》2018,63(4):463-471
We study a class of nonlinear elliptic problems with Navier boundary condition and involving the Laplace and the biharmonic operators. The main result of this paper establishes a sufficient condition for the existence of nontrivial weak solutions, in relationship with the values of a certain real parameter with respect to the principal eigenvalue of the Laplace operator. 相似文献
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The notion of a microbundle was introduced in the 1960s but the theory came to an abrupt halt when it was shown that for a metrisable manifold, microbundles are equivalent to fibre bundles. In this paper we consider microbundles over non-metrisable manifolds. In some cases microbundles are equivalent to fibre bundles but in others they are not. In particular, we show that a manifold is metrisable if and only if its tangent microbundle is equivalent to a fibre bundle. We also illustrate that for some non-metrisable manifolds every trivial microbundle contains a trivial fibre bundle whereas other manifolds may support a trivial microbundle not containing a trivial fibre bundle.