Abstract : In the first part of this talk we will show how classical tools of Riemannian geometry can be used in the setting of stratfied spaces in order to obtain a lower bound for the spectrum of the Laplacian, under an appropriate assumption of positive curvature. Such assumption involves the Ricci tensor on the regular set and the angle along the stratum of codimension 2. We then show that a rigidity result holds when the lower bound for the spectrum is attained. These results, restricted to compact smooth manifolds, give a well-known theorem by M. Obata and A. Lichnerowicz.
Finally, we will explain some consequences of the previous theorems on the existence of a conformal metric with constant scalar curvature on a stratified space.