Inverse Function Theorems and Jacobiansover Metric Spaces

Abstract

We present inversion results for Lipschitz maps f : Ω ⊂ ℝN → (Y, d) and stability of inversion for uniformly convergent sequences. These results are based on the Area Formula and on the l.s.c. of metric Jacobians.

New inverse and implicit function theorems for differentiable maps with isolated critical points

“…Let us recall a concept [6,24]: a map H between two topological spaces is said to be discrete at a given point x 0 if there exists an open neighborhood of x 0 on which H assumes the value H(x 0 ) only at x 0 . Theorem 1.2 then means that Euclidean vector fields with isolated critical points are discrete maps.…”