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AFEM for Geometric PDE: The Laplace-Beltrami Operator
2013We 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 +3 more
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Eigenvalues of the Laplace-Beltrami operator on a prolate spheroid
Journal of Differential Equations, 2023The 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, 2013AbstractIn 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 +4 more
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Laplace-beltrami operators of measures on banach spaces
Acta Mathematica Sinica, 1986Let 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
2017In 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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ON THE RESOLVENT OF THE LAPLACE–BELTRAMI OPERATOR IN HYPERBOLIC SPACE
Journal of the Australian Mathematical Society, 2015In 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, 1995The 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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On the square root of the Laplace--Beltrami operator as a Hamiltonian
Classical and Quantum Gravity, 1994Summary: The Einstein equations for a spacetime of the form \(T^ 2 \times \mathbb{R}\) can be reduced to a Hamiltonian system on the Teichmüller space. However, the resulting Hamiltonian is the square root of the quadratic form in the momenta. Trying to make sense of this as a quantum operator is problematic since the Hamiltonian operator would be non ...
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Spectrum of the Laplace–Beltrami Operator on Antisymmetric Functions
Journal of Mathematical ScienceszbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Gamma-convergence of Laplace-Beltrami operators in the plane
2000A mapping \(f:\Omega\to\mathbb{R}^2\) from a plane domain has finite distortion if \(f\in W^{1,2}(\Omega)\) and \(|f'(x)|^2\leq K(x) J(x,f)\) a.e.
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