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A short note on rigidity of compact surfaces in space forms

Volume 70 / 2022

Wagner Oliveira Costa-Filho Bulletin Polish Acad. Sci. Math. 70 (2022), 159-164 MSC: Primary 53C40; Secondary 53C20, 53C42. DOI: 10.4064/ba220613-19-3 Published online: 14 April 2023


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.


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