Are you looking for information about a lecture or an event? Here you can find all the past activities as well as specific information about a visitor or event.

When? No restrictions
Year
Years: From to

Order
Type Talk:

Event:

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

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)

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

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)