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Showing 1 to 9 of 9 for “"Laplace Beltrami Operator"”.
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Computing Eigenmodes of Elliptic Operators on Manifolds Using Radial Basis Functions
… methods is proposed to obtain eigenmodes of Laplace-Beltrami operator on manifolds, and its performance is compared against existing alternative methods. Radial Basis Function (RBF)-based methods allow one to obtain interpolation and differentiation matrices easily by using scattered data …
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Steklov geometry processing : an extrinsic approach to spectral shape analysis
We propose using the Dirichlet-to-Neumann operator as an extrinsic alternative to the Laplacian for spectral geometry processing and shape analysis. Intrinsic approaches, usually based on the Laplace-Beltrami operator, cannot capture the spatial embedding of a shape up to rigid motion, and many …
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Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an observer on the boundary of the manifold when the manifold is set into motion …
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The noncommutative geometry of ultrametric cantor sets
… is then taken further and an analogue of the Laplace-Beltrami operator is created for an ultrametric Cantor set. The Laplacian then allows to create an analogue of Brownian motion generated by this Laplacian. All these tools are then applied to the triadic Cantor set. Other examples of …
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CLASSIFICATION RESULTS FOR SEMILINEAR ELLIPTIC EQUATIONS
… it is proved that the Neumann eigenvalues of the Laplace Beltrami operator on D play a role in computing the Morse index. The second one is about a similar breaking of symmetry result, obtained for positive solutions of the critical Neumann problem in the whole unbounded cone. In this case, it is …
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A posteriori error estimates for the Poisson problem on closed, two-dimensional surfaces
… curved surface, the Poisson Problem features the Laplace-Beltrami Operator, which is a generalization of the Laplacian and specific to the surface where the problem is being solved. A Finite Element Method for solving the Poisson Problem on a closed surface has been described and shown to converge …
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Nodal geometry of eigenfunctions on smooth manifolds and hardy-littlewood-sobolev inequalities on the heisenberg group
… on M:</p> <p>-Δu=Λu,</p> <p>in which Δ is the Laplace-Beltrami operator. That is, u is an eigenfunction with eigenvalue Λ. We analyze the asymptotic behavior of eigenfunctions as Λ go to ∞ (i.e., limit of high energy states) in terms of the following aspects.</p> <p>(1) Local and global …
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Geometric Computing beyond the Laplacian
The Laplace–Beltrami operator, or, Laplacian, is the central object of study in shape analysis, geometry processing, and scientific computing. Motivated by the ubiquity of Laplacian in geometric computing algorithms, this thesis initiates a program for systematically designing novel algorithms by …
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Global Existence of solutions to Reaction-Diffusion Systems with Mass Transport type Boundary Conditions
We consider coupled reaction-diffusion models, where some components react and diffuse on the boundary of a region, while other components diffuse in the interior and react with those on the boundary through mass transport. We proved if vector fields are locally Lipschitz functions and satisfies …