相关论文: On stable constant mean curvature surfaces in S2 X…

In this paper, we study stable constant mean curvature $H$ surfaces in $\R^3$. We prove that, in such a surface, the distance from a point to the boundary is less that $\pi/(2H)$. This upper-bound is optimal and is extended to stable…

For constant mean curvature surfaces of class $C^2$ immersed inside Sasakian sub-Riemannian 3-manifolds we obtain a formula for the second derivative of the area which involves horizontal analytical terms, the Webster scalar curvature of…

We prove that a strictly stable constant-mean-curvature hypersurface in a smooth manifold of dimension less than or equal to 7 is uniquely homologically area minimizing for fixed volume in a small L^1 neighborhood.

We prove that the stable 2-systole is uniformly bounded on the space of Riemannian metrics with scalar curvature at least one for closed spin 2-essential manifolds, which includes $S^2 \times S^2$, $S^2 \times T^n$, and…

The total mean curvature functional for submanifolds into the Riemannian product space $\mathbb{S}^n\times\mathbb{R}$ is considered and its first variational formula is presented. Later on, two second order differential operators are…

In this paper, we present two rigidity results for stable constant mean curvature (CMC) surfaces immersed in $3$-manifolds with positive scalar curvature, assuming that the Hawking mass is zero. In the first result, we assume the surface to…

We make observations about constant mean curvature surfaces in Euclidean 3-space and their dual surfaces, and the resulting pairs of surfaces in hyperbolic 3-space under the Lawson correspondence.

In this paper we study the r-stability of closed spacelike hypersurfaces with constant $r$-th mean curvature in conformally stationary spacetimes of constant sectional curvature. In this setting, we obtain a characterization of…

We classify the hypersurfaces of dimension n >= 3 with constant sectional curvature in the product spaces R^k x S^{n-k+1} and R^k x H^{n-k+1}, for 2 <= k <= n-1. Our results provide a complete description of these hypersurfaces and extend…

In this paper we study the strong stability of spacelike hypersurfaces with constant $r$-th mean curvature in Generalized Robertson-Walker spacetimes of constant sectional curvature. In particular, we treat the case in which the ambient…

We study metric invariants of Riemannian manifolds $X$ defined via the $\mathbb T^\rtimes$-stabilized scalar curvatures of manifolds $Y$ mapped to $X$ and prove in some cases additivity of these invariants under Riemannian products…

It is still an open question whether a compact embedded hypersurface in the Euclidean space R^{n+1} with constant mean curvature and spherical boundary is necessarily a hyperplanar ball or a spherical cap, even in the simplest case of…

Surfaces with constant mean curvature (CMC) are critical points of the area with volume constraint. They serve as a mathematical model of surfaces of soap bubbles and tiny liquid drops. CMC surfaces are said to be stable if the second…

A gap in the proof prevents us to show that surfaces with constant mean curvature closed to 1/2 in H2 X R and having boundary with curvature greater than one, contained in a horizontal section P of H2 X R are topological disks, provided…

We study the global behavior of (weakly) stable constant mean curvature hypersurfaces in general Riemannian manifolds. By using harmonic function theory, we prove some one-end theorems which are new even for constant mean curvature…

We study some properties of mean curvature flow solitons in general Riemannian manifolds and in warped products, with emphasis on constant curvature and Schwarzschild type spaces. We focus on splitting and rigidity results under various…

We study stable surfaces, i.e., second order minima of the area for variations of fixed volume, in sub-Riemannian space forms of dimension $3$. We prove a stability inequality and provide sufficient conditions ensuring instability of…

A surface of constant mean curvature (CMC) equal to $H$ in a sub-Riemannian $3$-manifold is strongly stable if it minimizes the functional $\text{area}+2H\,\text{volume}$ up to second order. In this paper we obtain some criteria ensuring…

Let $M$ be an orientable surface immersed in the De Sitter space $S_1^3$ in $R^4_1$ or anti de Sitter space $H_1^3$ in $R^4_2$. In the case that $M$ is of $L_1$-2-type we prove that the following conditions are equivalent to each other: $M$…

We find out upper bounds for the first eigenvalue of the stability operator for compact constant mean curvature surfaces immersed into certain 3-dimensional Riemannian spaces, in particular into homogeneous 3-manifolds. As an application we…