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a lot of deformations in real-world can be characterized as an isometry or a near-isometry, the isometry invariance property of the eigenvalues of the Laplace – Beltrami operator gives advantage for many ...
, where |$\Delta$| is the Laplace – Beltrami operator of |$M$|. The Steklov spectrum |$0=\sigma_1\le\sigma_2\le\cdots\nearrow\infty$| is discrete, non-negative and unbounded, and each eigenvalue has finite ...
without boundary. Given a Riemannian metric $$g$$ on $$\Sigma$$, the spectrum of $$\Delta_g = -div_g \nabla$$, the Laplace - Beltrami operator , is a sequence 0=λ0 ...
shape space differences that characterize morphological variation expressed as area-based and conformal operators . Note that the GDPF step here subsamples shape at a low resolution with only 128 and 256 ...
}$$ for $$\gamma \in (0,n/2)$$. The main idea used in [9] is to relate the extension problem for the Laplacian on $$\mathbb{R}^n$$ to the scattering theory for the Laplace – Beltrami operator on the hyperbolic space ...
Kernel Asymptotic and |$\boldsymbol{\det'\Delta}$| Let |$\Delta$| stand for the Friedrichs extension of the Laplace – Beltrami operator on |$(X, f^*\mathsf m)$|. The asymptotic of |$\operatorname{Tr} e ...
measures such as Laplace - Beltrami spectra and Zernike moments, and (4) application of Mindboggle to provide the most detailed shape measures computed on human brain image data. This Introduction provides ...
whose behaviours in the near-field are directly related to the eigenvalues of the Laplace – Beltrami operator . This is important since the correct near-field behaviour at the tip of the quarter-plane had so ...
$| is an approximation of |$ g $|. Following Ciarlet (2002, Chap. 4), we define conforming space discretizations. For that purpose, it is convenient to write the operators as bilinear forms. We denote the bilinear form ...
$| be an oriented compact higher graph manifold, then there exists a |$p\geq 0$|, such that zero belongs to the spectrum of the Laplace – Beltrami operator |$\Delta_{p}$| acting on square-integrable |$p$|-forms ...
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