A Measure on the space of Lipschitz isometric maps of a compact 1-manifold into ${\mathbb{R}}^2$

Amites Dasgupta, Mahuya Datta

Let $M$ be a compact 1-manifold. Given a continuous function $g:M\to {\mathbb{R}}_{+}$ we consider the following ordinary differential equation: $\Vert \dot{f}(t)\Vert =g(t)$, where $f:M\to \ma…