Related papers: Stable $s$-minimal cones in $\mathbb{R}^2$ are fla…

We consider the isoperimetric inequality involving the $s$-perimeter and the $t$-perimeter with $0<s<t<1$, and show that the ball is a local minimizer of the (scale-invariant) isoperimetric ratio $\mathcal{F}(E):=P_t(E)^{\frac{1}{n-t}}/…

This paper investigates the long-term orbital stability of small bodies near the central binary of the Alpha Centauri system. Test particles on circular orbits are integrated in the field of this binary for 32000 binary periods or…

In this paper, we study planar nonlocal Delaunay sets. That is, open sets in $\mathbb{R}^2$ with constant nonlocal mean curvature that are periodic in $x_1$, and even in $x_1$ and in $x_2$. Using bifurcation analysis and fine explicit…

We study the linear and nonlinear stability of relative equilibria in the planar N-vortex problem, adapting the approach of Moeckel from the corresponding problem in celestial mechanics. After establishing some general theory, a topological…

We prove a sharp stable $2$-systolic inequality for complex projective space under the scalar curvature lower bound of the normalized Fubini-Study metric. If $M$ is diffeomorphic to $\mathbb{C}\mathrm{P}^n$ and $\mathrm{scal}_g\ge 4n(n+1)$,…

The Gauss map $g$ of a surface $\Sigma$ in $\mathbb{R}^4$ takes its values in the Grassmannian of oriented 2-planes of $\mathbb{R}^4$: $G^+(2,4)$. We give geometric criteria of stability for minimal surfaces in $\mathbb{R}^4$ in terms 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.

In this paper we establish new characterizations of stable derivators, thereby obtaining additional interpretations of the passage from (pointed) topological spaces to spectra and, more generally, of the stabilization. We show that a…

We study the problem of existence of regions separating a given amount of volume with the least possible perimeter inside a Euclidean cone. Our main result shows that nonexistence for a given volume implies that the isoperimetric profile of…

We find classically stable solitons (instantons) in odd (even) dimensional scalar noncommutative field theories whose scalar potential, $V(\ph)$, has at least two minima. These solutions are bubbles of the false vacuum whose size is set by…

In this paper we consider a partial overdetermined mixed boundary value problem in domains inside a cone as in [18]. We show that in cones having an isoperimetric property the only domains which admit a solution and which minimize a…

We prove that there are no minimal hypersurfaces properly immersed in any region of the Euclidean space bounded by unstable minimal cones. We also prove the analogous result for $r$-minimal hypersurfaces.

Consider the energy $E_\alpha[\Sigma]=\int_\Sigma |p|^\alpha\, d\Sigma$, where $\Sigma$ is a surface in Euclidean space $\r^3$ and $\alpha\in\r$. We prove that planes and spheres are the only stationary surfaces for $E_\alpha$ with constant…

For any smooth projective variety $X$ of dimension $n$ over an algebraically closed field $k$ of characteristic $p>0$ with $\mu(\Omega^1_X)>0$. If ${\rm T}^{\ell}(\Omega^1_X)$ ($0<\ell<n(p-1)$) are semi-stable, then the sheaf $B^1_X$ of…

The nonlinear Schroedinger equation possesses three distinct six-parameter families of complex-valued quasi-periodic travelling waves, one in the defocusing case and two in the focusing case. All these solutions have the property that their…

We calculate stable arrangements for a single superfluid vortex pinned to the wall of a stationary cylindrical container. We find that, independent of the details of the pinning site, stable vortices must subtend most of the cell…

Every $n th$ order monic polynomial corresponds $n$-dimensional vector. If the given polynomial is stable that is all its roots lie in the open left half plane it is said to be Hurwitz polynomial and the corresponding vector is called…

We classify minimal hypersurfaces in $R^n \times S^m$, $n,m \geq 2$, which are invariant by the canonical action of $O(n) \times O(m)$. We also construct compact and noncompact examples of invariant hypersurfaces of constant mean curvature.…

The relative isoperimetric inequality inside an open, convex cone $\mathcal C$ states that, at fixed volume, $B_r \cap \mathcal C$ minimizes the perimeter inside $\mathcal C$. Starting from the observation that this result can be recovered…

We investigate structural properties of the cone of roots of relative Steiner polynomials of convex bodies. We prove that they are closed, monotonous with respect to the dimension, and that they cover the whole upper half-plane, except the…