Related papers: Minimal area ellipses in the hyperbolic plane

Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…

We prove several results on the number of solutions to the asymptotic Plateau problem in $\mathbb H^3$. Firstly we discuss criteria that ensure uniqueness. Given a Jordan curve $\Lambda$ in the asymptotic boundary of $\mathbb H^3$, we show…

We show that for every $\epsilon>0$, there exists a compact lamination by $\epsilon$-holomorphic surfaces in the complex projective plane, minimal, and that carries hyperbolic holonomy. We call $\epsilon$-holomorphic a real 2-dimensional…

We show that for a family of randomly kicked Hamilton-Jacobi equations, the unique global minimizer is hyperbolic, almost surely. Furthermore, we prove the unique forward and backward viscosity solutions, though in general only Lipshitz,…

We study a variational problem for the perimeter associated with the Grushin plane, called minimal partition problem with trace constraint. This consists in studying how to enclose three prescribed areas in the Grushin plane, using the…

Given a closed Riemannian manifold of dimenion less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the…

We determine optimal inequalities for the systole of all hyperbolic compact surfaces of caracteristic -1. First, we study the geometry and topology of these surfaces. Then, we describe the action of modular groups on Teichm\"{u}ller spaces.…

We consider the helical reduction of the wave equation with an arbitrary source on $(n+1)$-dimensional Minkowski space, $n\geq2$. The reduced equation is of mixed elliptic-hyperbolic type on ${\bf R}^n$. We obtain a uniqueness theorem for…

We define and prove the existence of unique solutions of an asymptotic Plateau problem for spacelike maximal surfaces in the pseudo-hyperbolic space of signature (2, n): the boundary data is given by loops on the boundary at infinity of the…

We give an a priori bound on the (n-7)-dimensional measure of the singular set for an area-minimizing n-dimensional hypersurface, in terms of the geometry of its boundary.

The energies of low-lying bound states of a microscopic quantum many-body system of particles can be worked out in a reduced Hilbert space. We present here and test a specific non-perturbative truncation procedure. We also show that real…

We show that if the eccentricity of an ellipse is sufficiently small then up to isometries it is spectrally unique among all smooth domains. We do not assume any symmetry, convexity, or closeness to the ellipse, on the class of domains. In…

We propose a simple derivation of an upper bound for the perimeter of an ellipse. The procedure, which relies on the use of elliptic integrals, consists in introducing, via inequalities and convexity properties, specific integrals which can…

We find the explicit local models of isolated singularities of conformal hyperbolic metrics by Complex Analysis, which is interesting in its own and could potentially be extended to high-dimensional case.

We continue the variational approach to parabolic trajectories introduced in our previous paper [5], which sees parabolic orbits as minimal phase transitions. We deepen and complete the analysis in the planar case for homogeneous singular…

The aim of this work is to study how the asymptotic boundary of a minimal hypersurface in H^nxR determines the behavior of the hypersurface at finite points, in several geometric situations.

We develop a bubble-compactness theory for embedded CMC hypersurfaces with bounded index and area inside closed Riemannian manifolds in low dimensions. In particular we show that convergence always occurs with multiplicity one, which…

Initiated by the work of Uhlenbeck in late 1970s, we study questions about the existence, multiplicity and asymptotic behavior for minimal immersions of closed surface in some hyperbolic three-manifold, with prescribed conformal structure…

We find the first examples of triply periodic minimal surfaces of which the intrinsic symmetries are all of horizontal type.

In hyperbolic space density cannot be defined by a limit as we define it in Euclidean space. We describe the local density bounds for sphere packings and we discuss the different attempts to define optimal arrangements in hyperbolic space.