First \(\frac{2}{n}\)-stability eigenvalue of singular minimal hypersurfaces in space forms
If \(M\) is a minimal hypersurface in a space form \(\overline{M}^{n+1}(c)\) and \(A\) is its second fundamental form, then \(M\) is said to be \(\frac2n\)-\textit{stable} when for all \(f\in C^\infty_0(M)\) the integral \[\int_M (\| \nabla f\|^2 - \frac{n-2}{n}(\| A\|^2 + cn)f^2)\] is nonnegative. In this paper, the authors study such stability on singular minimal hypersurfaces in space forms and provide a characterization of catenoids in space forms in terms of this stability.
scientific article; zbMATH DE number 7606041
scientific article