In differential geometry there are a number of second-order, linear, elliptic differential operators bearing the name Laplacian. This article provides...

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

manifold has been most intensively studied, although other Laplace operators in differential geometry have also been examined. The field concerns itself with...

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

{n}{k}}={\tbinom {n}{n-k}}} . The naturalness of the star operator means it can play a role in differential geometry, when applied to the cotangent bundle of a pseudo-Riemannian...

In mathematics, stochastic analysis on manifolds or stochastic differential geometry is the study of stochastic analysis over smooth manifolds. It is therefore...

in striking contrast to the case of ordinary differential equations (ODEs) roughly similar to the Laplace equation, with the aim of many introductory textbooks...

change in time. They are also important in pure mathematics, where they are fundamental to various fields of research such as differential geometry and optimal...

In mathematics, the differential geometry of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most...

harmonic with respect to the Laplace-Beltrami operator for the standard round metric on the sphere: the only harmonic functions in this sense on the sphere...

p-Laplacian Laplace operators in differential geometry Young–Laplace equation Laplace invariant Laplace series (Fourier–Laplace series) Laplace expansion...

are built from them are called differential operators, integral operators or integro-differential operators. Operator is also used for denoting the symbol...

the partial differential equation. In applications to the physical sciences, operators such as the Laplace operator play a major role in setting up and...

In mathematics and in quantum mechanics, a Dirac operator is a first-order differential operator that is a formal square root, or half-iterate, of a second-order...

Differential Forms for Computational Modeling". In Bobenko, A.I.; Sullivan, J.M.; Schröder, P.; Ziegler, G.M. (eds.). Discrete Differential Geometry....

combinatorial optimization, digital geometry, discrete differential geometry, geometric graph theory, toric geometry, and combinatorial topology. Polyhedra...

using the Laplace operator, geometric smoothing might be achieved by convolving a surface geometry with a blur kernel formed using the Laplace-Beltrami...

A parabolic partial differential equation is a type of partial differential equation (PDE). Parabolic PDEs are used to describe a wide variety of time-dependent...

In differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal...

and plays a deep role in differential geometry via the Atiyah–Singer index theorem. Unbounded operators are also tractable in Hilbert spaces, and have...

role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering, especially in the...

complexes. It is used in the study of computer graphics, geometry processing and topological combinatorics. Discrete Laplace operator Discrete exterior calculus...

In differential geometry, the Atiyah–Singer index theorem, proved by Michael Atiyah and Isadore Singer (1963), states that for an elliptic differential...

problem Examples of differential equations Laplace transform applied to differential equations List of dynamical systems and differential equations topics...

star operator Weitzenböck identity Laplacian operators in differential geometry List of coordinate charts List of formulas in Riemannian geometry Christoffel...

In differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian...

\varphi } in Γ ( V ) {\displaystyle \Gamma (V)} and elements g in G. All linear invariant differential operators on homogeneous parabolic geometries, i.e....

combinatorics Continuous probability Differential entropy in information theory Differential games Differential geometry, the application of calculus to specific...

article summarizes several identities in exterior calculus, a mathematical notation used in differential geometry. The following summarizes short definitions...