Research proof index

The integral appearing in corrugations is periodic.

We are given a suitably nice extended metric space X and three local constraints P₀,P₀' and P₁ on maps from X to some type Y. All maps entering the discussion are required to statisfy P₀ everywhere. The goal is to turn a map f₀ satisfying P₁ near a compact set K into one satisfying everywhere without changing f₀ near K. The assumpt...

Homotopy of formal solutions obtained by successive corrugations in some landscape L to improve a formal solution 𝓕 until it becomes holonomic near L.K₀.

A corollary of the local parametric h-principle, forgetting the homotopy and ε-closeness, and just stating the existence of a solution that is holonomic near K. Furthermore, we assume that P = ℝ and K is of the form compact set × I. This is sufficient to prove sphere eversion.

Ampleness survives localization

Gromov's Theorem