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

Universidad de Granada

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 \(n\geq 4\). Moreover, we will show that there exist non-compact free boundary minimal hypersurfaces which are not totally geodesic, \(n\geq 8\), with Morse index equal to \(0\). Also, for \(n\geq 4\), there exist infinitely many non-compact free boundary minimal hypersurfaces, which are not congruent to each other, with infinite Morse index. Finally, we will discuss the density at infinity of a free boundary minimal hypersurface with respect to a minimal cone constructed over a minimal hypersurface of the unit Euclidean sphere. We obtain a lower bound for the density in terms of the area of the boundary of the hypersurface and the area of the minimal hypersurface in the unit sphere. This lower bound is optimal in the sense that only minimal cones achieve it.

Sala EINSTEIN UGR (virtual)

Contraseña/Password: 563155

A construction of constant mean curvature surfaces in \(\mathbb{H}^2\times \mathbb{R}\) and the Krust property

Universidad de Granada

In this talk we will construct via Daniel's sister correspondence in \(\mathbb{H}^2\times\mathbb{R}\) a \(2\)-parameter family of Alexandrov-embedded constant mean curvature \(0\,\)<\(\,H\leq 1/2\) surfaces in \(\mathbb{H}^2\times \mathbb{R}\) with \(2\) ends and genus \(0\). They are symmetric with respect to a horizontal slice and \(k\) vertical planes disposed symmetrically. We will discuss the embeddedness of the constant mean curvature surfaces of this family, and we will show that the Krust property does not hold for \(0\,\)<\(\,H\leq 1/2\); i.e, there are minimal graphs over convex domain in \(\widetilde{\text{SL}}_2(\mathbb{R})\) and \(\text {Nil}_3\) whose sister conjugate surface is not a vertical graph in \(\mathbb{H}^2\times\mathbb{R}\).

Sala CURIE UGR (virtual)

Contraseña/Password: 704464


X International Meeting on Lorentzian Geometry

Córdoba (Spain)

The meeting is intended for all kind of researchers with interest on Lorentz Geometry and its applications to General Relativity.
For PhD students the meeting will represent an ideal way to have their first contact with current research topics on the area. Furthermore, an advanced course given by an expert on the area will be organized.
For senior researchers, these meetings represent an ideal place where to exhibit their latest results and to create new ways of collaboration.