On non-compact free boundary minimal hypersurfaces in the Riemannian Schwarzschild spaces

Abstract: We will show that, in contrast with the 3-dimensional case, the Morse index of a free boundary rotationally symmetric totally geodesic hypersurface of the n-dimensional Riemannnian Schwarzschild space with respect to variations that are tangential along the horizon is zero, for n≥4. Moreover, we will show that there exist non-compact free boundary minimal hypersurfaces which are not totally geodesic, n≥8, with Morse index equal to zero. Also, for n≥4, there exist infinitely many non-compact free boundary minimal hypersurfaces, which are not congruent to each other, with infinite Morse index.

differential geometry

Audience: researchers in the topic

Geometric Analysis in the Large