A short note on rigidity of compact surfaces in space forms

A rigidity result for a compact (without boundary) surface in a space form is obtained under a certain condition involving the Gaussian curvature and mean curvature of the surface. Moreover, as a byproduct of our approach, we shall present an alternative proof of an extension of Li’s theorem (2001) due to Chang (2013), on an integral inequality for Willmore surfaces in space forms.