# When do the lengths of simple closed curves determine a hyperbolic surface?

Consider hyperbolic metrics on $$\Sigma_g$$ a closed orientable surface of genus $$g$$. Let $$[\gamma_1] , \cdots, [\gamma_n]$$ be a finite collection of isotopy classes of simple closed curves on $$\Sigma_g$$.

At what conditions on $$[\gamma_1] , \cdots, [\gamma_n]$$ is any (isotopy class of) metric completely determined by the lengths of the geodesic representatives of respective classes $$[\gamma_1] , \cdots, [\gamma_n]$$ ?