In differential geometry, the Laplace–Beltrami operator is a generalization of the Laplace operator to functions defined on submanifolds in Euclidean...

In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on Euclidean...

In mathematics, the discrete Laplace operator is an analog of the continuous Laplace operator, defined so that it has meaning on a graph or a discrete...

tensors of rank 0), the connection Laplacian is often called the Laplace–Beltrami operator. It is defined as the trace of the second covariant derivative:...

functions on the sphere which are harmonic with respect to the Laplace-Beltrami operator for the standard round metric on the sphere: the only harmonic...

fashion, the equation can be written in terms of the intrinsic Laplace–Beltrami operator Δ L B = 1 f 2 Δ 0 {\displaystyle \Delta _{\mathrm {LB} }={\frac...

eigenfunctions) of the Laplace–Beltrami operator to compare and analyze geometric shapes. Since the spectrum of the Laplace–Beltrami operator is invariant under...

y 2 {\displaystyle ds^{2}=E\,dx^{2}+2F\,dx\,dy+G\,dy^{2}} and Laplace–Beltrami operator Δ f = 1 H ( ∂ x G H ∂ x f − ∂ x F H ∂ y f − ∂ y F H ∂ x f + ∂...

theorem Yamabe problem Killing vector field Hodge star operator Weitzenböck identity Laplacian operators in differential geometry List of coordinate charts...

Weyl's law describes the asymptotic behavior of eigenvalues of the Laplace–Beltrami operator. This description was discovered in 1911 (in the d = 2 , 3 {\displaystyle...