Editing Homotopy principle (section)

[[File:MorinSurfaceAsSphere'sInsideVersusOutside.PNG|thumb|The homotopy principle generalizes such results as Smale's proof of [[sphere eversion]].]]

In [[mathematics]], the '''homotopy principle''' (or '''h-principle''') is a very general way to solve [[partial differential equation]]s (PDEs), and more generally [[partial differential relation]]s (PDRs).  The h-principle is good for [[underdetermined system|underdetermined]] PDEs or PDRs, such as the immersion problem, isometric immersion problem, fluid dynamics, and other areas.

The theory was started by [[Yakov Eliashberg]], [[Mikhail Gromov (mathematician)|Mikhail Gromov]] and Anthony V. Phillips. It was based on earlier results that reduced partial differential relations to [[homotopy]], particularly for immersions. The first evidence of h-principle appeared in the [[Whitney–Graustein theorem]]. This was followed by the Nash–Kuiper isometric ''C''<sup>1</sup> embedding theorem and the Smale–Hirsch immersion theorem.