Results 151 to 160 of about 775 (185)

Simplification of the Laplace–Beltrami operator

Mathematics and Computers in Simulation, 2000
Abstract The zonal polynomials are symmetric polynomial functions each of which is an eigenfunction of a kind of Laplace–Beltrami operator. We give a simplification of the Laplace–Beltrami operator. We realize a symbolic algorithm for obtaining the coefficients of zonal polynomials.
Hiroki Hashiguchi, Shigekazu Nakagawa, Naoto Niki   +2 more
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On the nature of the laplace–beltrami operator on lipschitz manifolds

Journal of Mathematical Sciences, 2010
The paper under review is concerned with several qualitative properties of the Laplace-Beltrami operator on Lipschitz surfaces and on Lipschitz manifolds. The authors establish related invertibility properties, as well as results on the nature of the spectrum and the regularity of eigenfunctions.
Gesztesy, F., Mitrea, I., Mitrea, D., Mitrea, M.   +3 more
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Eigenvalues of the Laplace-Beltrami operator on a prolate spheroid

Journal of Differential Equations, 2023
The Laplace-Beltrami operator is a mathematical operator used in differential geometry to study the curvature and geometry of surfaces and manifolds. It measures the Laplacian of a function defined on a surface, providing valuable insights into the intrinsic properties of the surface. The Laplace-Beltrami operator on a prolate spheroid allows for a set
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Mesh‐Free Discrete Laplace–Beltrami Operator

Computer Graphics Forum, 2013
AbstractIn this work we propose a new discretization method for the Laplace–Beltrami operator defined on point‐based surfaces. In contrast to the existing point‐based discretization techniques, our approach does not rely on any triangle mesh structure, turning out truly mesh‐free.
Fabiano Petronetto, Afonso Paiva 0001, Elias S. Helou, David E. Stewart, Luis Gustavo Nonato   +4 more
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AFEM for Geometric PDE: The Laplace-Beltrami Operator

2013
We present several applications governed by geometric PDE, and their parametric finite element discretization, which might yield singular behavior. The success of such discretization hinges on an adequate variational formulation of the Laplace-Beltrami operator, which we describe in detail for polynomial degree 1.
Bonito, Andrea, Cascón, José Manuel, Morin, Pedro, Nochetto, Ricardo Horacio   +3 more
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ON THE RESOLVENT OF THE LAPLACE–BELTRAMI OPERATOR IN HYPERBOLIC SPACE

Journal of the Australian Mathematical Society, 2015
In this paper, a detailed description of the resolvent of the Laplace–Beltrami operator in $n$-dimensional hyperbolic space is given. The resolvent is an integral operator with the kernel (Green’s function) being a solution of a hypergeometric differential equation. Asymptotic analysis of the solution of this equation is carried out.
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Multiplicities of singularities of eigenfunctions for the Laplace—Beltrami operator

Functional Analysis and Its Applications, 1995
The author deals with the multiplicities of singularities of eigenfunctions for the Laplace-Beltrami operator. Let \(M\) be a smooth compact 2-dimensional Riemann manifold. Let \(\chi(M)\) be the Euler characteristic of the manifold \(M\). Let \(f_N\) be the eigenfunction of the Laplace-Beltrami operator on \(M\) with index \(N\).
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Laplace-beltrami operators of measures on banach spaces

Acta Mathematica Sinica, 1986
Let X be a separable Banach space, \(X^*\) be its dual and B(X) be its Borel field, where a probability measure \(\mu\) is given. The main results are the following: Theorem 1. Let \(\mu\) be ergodic w.r.t. Q, the set of all quasi-invariant directions of \(\mu\), and symmetric and \(X^*\subset L^ 2(X,\mu)\), then we can find a sequence \((a_ n)\) such ...
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The Hyperbolic Laplace-Beltrami Operator

2017
In this chapter we will introduce some basic concepts of hyperbolic geometry and automorphic forms. A variety of books is available which provide a more comprehensive description of the relevant material. Hejhal’s books about the Selberg trace formula [58] and [59] are a source of exhaustive informations regarding most topics discussed in this chapter,
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Perturbations of the Laplace-Beltrami Operator

2011
PerTurbo: A New Classification Algorithm Based on the Spectrum Perturbations of the Laplace-Beltrami ...
Courty, Nicolas, Burger, Thomas, Laurent, Johann   +2 more
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