Related papers: Stable hypersurfaces with constant higher order me…

This paper explains the construction of all hypersurfaces with constant mean curvature -- cmc -- and exactly two principal curvatures on any space form endowed with a semi-riemannian metric. Here we will consider riemannian hypersurfaces as…

Defined mathematically as critical points of surface area subject to a volume constraint, constant mean curvatures (CMC) surfaces are idealizations of interfaces occurring between two immiscible fluids. Their behavior elucidates phenomena…

The (n+1)-sphere contains a simple family of constant mean curvature (CMC) hypersurfaces which are products of lower-dimensional spheres called the generalized Clifford hypersurfaces. This paper demonstrates that new, topologically…

Let $M^n$ be a biharmonic hypersurface with constant scalar curvature in a space form $\mathbb M^{n+1}(c)$. We show that $M^n$ has constant mean curvature if $c>0$ and $M^n$ is minimal if $c\leq0$, provided that the number of distinct…

Let $\phi:M\to\mathbb{S}^{n+1}\subset\mathbb{R}^{n+2}$ be an immersion of a complete $n$-dimensional oriented manifold. For any $v\in\mathbb{R}^{n+2}$, let us denote by $\ell_v:M\to\mathbb{R}$ the function given by $\ell_v(x)=\phi(x),v$ and…

In this paper we prove some general results on constant mean curvature lamination limits of certain sequences of compact surfaces $M_n$ embedded in $\mathbb R^3$ with constant mean curvature $H_n$ and fixed finite genus, when the boundaries…

We prove existence and stability of smooth entire strictly convex spacelike hypersurfaces of prescribed Gauss curvature in Minkowski space. The proof is based on barrier constructions and local a priori estimates.

In this paper we study sets in the $n$-dimensional Heisenberg group $\hhn$ which are critical points, under a volume constraint, of the sub-Riemannian perimeter associated to the distribution of horizontal vector fields in $\hhn$. We define…

In this paper, we investigate the preservability of the curvature-adaptedness along the mean curvature flow starting from a compact curvature-adapted hypersurface in locally symmetric spaces, where the curvature-adaptedness means that the…

We discuss the validity of Minkowski integral identities for hypersurfaces inside a cone, intersecting the boundary of the cone orthogonally. In doing so we correct a formula provided in [3]. Then we study rigidity results for constant mean…

We approach the one-parameter family of rotational constant mean curvature (CMC) spheres of $\mathbb H^n\times\mathbb R$ and $\mathbb S^n\times\mathbb R$ focusing on their stability and isoperimetry properties. We prove that all rotational…

In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to…

In this paper we investigate the connection between the index and the geometry and topology of capillary surfaces. We prove an index estimate for compact capillary surfaces immersed in general 3-manifolds with boundary. We also study…

We consider a complete biharmonic hypersurface with nowhere zero mean curvature vector field $\phi:(M^m,g)\rightarrow (S^{m+1},h)$ in a sphere. If the squared norm of the second fundamental form $B$ is bounded from above by m, and $\int_M…

In this paper, we characterize and classify the isoparametric hypersurfaces with constant principal curvatures in the product spaces $ \mathbb{Q}^{2}_{c_{1}} \times \mathbb{Q}^{2}_{c_{2}}$, where $\mathbb{Q}^{2}_{c_{i}}$ is a space form…

We study the principal curvatures of properly embedded constant mean curvature hypersurfaces in the Anti-de Sitter space $\mathbb{H}^{n,1}$. We generalize the notion of convex hull and give an upper bound on the principal curvatures which…

We study rotational hypersurfaces with constant Gauss-Kronecker curvature. We solve the ODE for the generating curves of such hypersurfaces and analyze several geometric properties of such hypersurfaces. In particular, we discover a class…

In this article, we consider $\mathcal{C}^\infty$-smooth real hypersurfaces of infinite type in $\mathbb C^2$. The purpose of this paper is to give explicit descriptions for stability groups of the hypersurface $M(a,\alpha,p,q)$ (see Sec.…

We prove nonlinear stability for a large class of solutions to the Einstein equations with a positive cosmological constant and compact spatial topology in arbitrary dimensions, where the spatial metric is Einstein with either positive or…

We prove that any piece of a rotational hypersurface with prescribed mean curvature function in a Euclidean space can be uniquely extended infinitely, which generalizes the results by Euler and Delaunay for surfaces of revolution with…