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 geometry to the physics of general relativity, a Cauchy surface is usually interpreted as defining an "instant of time"; in the mathematics of general relativity, Cauchy surfaces are important in the formulation of the Einstein equations as an evolutionary problem. They are named for French mathematician Augustin-Louis Cauchy (1789-1857) due to their relevance for the Cauchy problem of general relativity.