In the mathematical field of Lorentzian geometry, a Cauchy surface is a certain kind of submanifold of a Lorentzian manifold. In the application of Lorentzian...

Augustin-Louis Cauchy. For a partial differential equation defined on Rn+1 and a smooth manifold S ⊂ Rn+1 of dimension n (S is called the Cauchy surface), the...

equations Cauchy–Schwarz inequality Cauchy sequence Cauchy surface Cauchy's theorem (geometry) Cauchy's theorem (group theory) Maclaurin–Cauchy test His...

In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis. It expresses the fact that a...

continuum mechanics, the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true stress...

inequality Cauchy sequence Uniformly Cauchy sequence Cauchy space Cauchy surface Cauchy's mean value theorem Cauchy stress tensor Cauchy's theorem (geometry)...

occur on light-like or null surfaces. An example might be found in certain types of black hole interiors, such as the Cauchy horizon of a charged (Reissner–Nordström)...

relativity states complete knowledge of the universe on a spacelike Cauchy surface can be used to calculate the complete state of the rest of spacetime...

vent at the top of Omega Cauchy is called Donna. To the south of Cauchy is a 120-km fault in the surface named the Rupes Cauchy, which forms a series of...

three-dimensional Cauchy surface, and furthermore that any two Cauchy surfaces for M are diffeomorphic. In particular, M is diffeomorphic to the product of a Cauchy surface...

everywhere on a spacelike three-dimensional hypersurface, called the Cauchy surface). Failure of the cosmic censorship hypothesis leads to the failure of...

in general relativity can be posed as an initial value problem on a Cauchy surface. There is a hierarchy of causality conditions, each one of which is...

disjoint from I + [ S ] {\displaystyle I^{+}[S]} . A Cauchy surface is a closed achronal set whose Cauchy development is M {\displaystyle M} . A metric is...

Cauchy's theorem is a theorem in geometry, named after Augustin Cauchy. It states that convex polytopes in three dimensions with congruent corresponding...

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with...

The Cauchy momentum equation is a vector partial differential equation put forth by Cauchy that describes the non-relativistic momentum transport in any...

a topological characterization of globally hyperbolic spacetimes. A Cauchy surface can possess corners, and thereby need not be a differentiable submanifold...

mathematics, the Crofton formula, named after Morgan Crofton (1826–1915), (also Cauchy-Crofton formula) is a classic result of integral geometry relating the length...

introducing the notions of stress and strain. Cauchy observed that the force across an imaginary surface was a linear function of its normal vector; and...

In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem (a particular boundary value problem of the theory...

is a Cauchy horizon. M-H spacetimes correspond to black holes which live forever and have an inner horizon. The inner horizon is the Cauchy surface. The...

this limitation, Park et al. (2006) proposed a surface Cauchy–Born rule. Several modified forms of the Cauchy–Born rule have also been proposed to cater to...

field theory and so one can require that Σ be a Cauchy surface, in fact, a state can be defined on any surface. Σ is of codimension one, and so one may cut...

developed by Colin Maclaurin and Augustin-Louis Cauchy and is sometimes known as the Maclaurin–Cauchy test. Consider an integer N and a function f defined...

universe (where "a particular moment in the universe" refers to a chosen Cauchy surface).: 188–207  There have been other attempts to formulate a theory that...

the derivatives of the Gauss map. If the projected Gauss map obeys the Cauchy–Riemann equations then either the trace vanishes or every point of M is...

In mathematics, the Cauchy condensation test, named after Augustin-Louis Cauchy, is a standard convergence test for infinite series. For a non-increasing...

general continuum mechanics and not only to hydrodynamics we start from the Cauchy momentum equation in its dimensionless (nondimensional) form. In order to...

which is globally hyperbolic, for which Σ {\displaystyle \Sigma } is a Cauchy surface (i.e. all past events influence what happens on Σ {\displaystyle \Sigma...

of surfaces deals with the differential geometry of smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have...