The Laplace–Beltrami operator, a fundamental object associated with Riemannian manifolds, encodes all intrinsic geometry of manifolds and has many desirable properties. Recently, we proposed the point integral method (PIM), a novel numerical method for discretizing the Laplace–Beltrami operator on point clouds (Li et al. in Commun Comput Phys 22(1):228–258, 2017). In this paper, we analyze the ...

In this paper we study Lipschitz regularity of elliptic PDEs on geometric graphs, constructed from random data points. The points are sampled a distribution supported smooth manifold. family equations that arises in analysis the context graph-based learning and contains, as important examples, satisfied by graph Laplacian eigenvectors. particular, prove high probability interior global estimate...

Abstract. The paper concerns numerical algorithms for solving the Beltrami equation fz̄(z) = μ(z)fz(z) for a compactly supported μ. First, we study an efficient algorithm that has been proposed in the literature, and present its rigorous justification. We then propose a different scheme for solving the Beltrami equation which has a comparable speed and accuracy, but has the virtue of a greater s...

For bicovariant differential calculi on quantum matrix groups a generalisation of classical notions such as metric tensor, Hodge operator, codifferential and Laplace-Beltrami operator for arbitrary k-forms is given. Under some technical assumptions it is proved that Woronowicz’ external algebra of left-invariant differential forms either contains a unique form of maximal degree or it is infinit...

In this paper, we study the problem of computing effective diffusivity for particles moving in chaotic flows. Instead solving a convection-diffusion type cell Eulerian formulation (arising from homogenization theory parabolic equations), compute motion Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). A robust numerical integrator based on splitting method wa...

A bstract The conformal symmetry algebra in 2D (Diff( S 1 )⊕Diff( )) is shown to be related its ultra/non-relativistic version (BMS 3 ≈GCA 2 ) through a nonlinear map of the generators, without any sort limiting process. For generic classical CFT , BMS generators then emerge as composites built out from chiral (holomorphic) components stress-energy tensor, T and $$ \overline{T} <mml:math xmlns:...

The Beltrami framework treats images as two dimensional manifolds embedded in a joint features-space domain. This way, a color image is considered to be a two dimensional surface embedded in a hybrid special-spectral five dimensional {x, y,R,G,B} space. Image selective smoothing, often referred to as a denoising filter, amounts to the process of area minimization of the image surface by mean cu...