Related papers: Asymptotics of high-codimensional area-minimizing …

We give an asymptotic equivalent at infinity of the unbounded solutions of some boundary layer equations arising in fluid mechanics.

We introduce and study co-dimension one area-minimizing locally rectifiable currents $T$ with $C^{1,\alpha}$ tangentially immersed boundary: $\partial T$ is locally a finite sum of orientable co-dimension two submanifolds which only…

In hyperbolic space $H^n$ we set a geodesic ball of radius $\rho$. Consider a $k$ dimensional minimal submanifold passing through the origin of the geodesic ball with boundary lies on the boundary of that geodesic ball. We prove that its…

We give a fairly complete solution to the asymptotic Plateau Problem for minimal surfaces in H^2xR. In particular, we identify the collection of finite Jordan curves in the asymptotic cylinder which bounds a minimal surface in H^2xR.

The solutions to surface evolution problems like mean curvature flow can be expressed as value functions of suitable stochastic control problems, obtained as limit of a family of regularised control problems. The control-theoretical…

We consider boundary value problems for quasilinear first-order one-dimensional hyperbolic systems in a strip. The boundary conditions are supposed to be of a smoothing type, in the sense that the $L^2$-generalized solutions to the…

We give sharp upper bounds on the injectivity radii of complete hyperbolic surfaces of finite area with some geodesic boundary components. The given bounds are over all such surfaces with any fixed topology; in particular, boundary lengths…

The asymptotic Dirichlet problem for harmonic maps from the hyperbolic plane into conformally compact Einstein manifolds is used to give a holographic characterization of conformal geodesics on the boundary at infinity, in a way deeply…

We consider an isothermal compressible fluid evolving on a cosmological background which may be either expanding or contracting toward the future. The Euler equations governing such a flow consist of two nonlinear hyperbolic balance laws…

We give a proof of an unpublished result of Thurston showing that given any hyperbolic metric on a surface of finite type with nonempty boundary, there exists another hyperbolic metric on the same surface for which the lengths of all simple…

In this paper we are concerned with the local well-posedness of the unsteady potential flows near a space corner of right angle, which could be formulated as an initial-boundary value problem of a hyperbolic equation of second order in a…

We consider a magnetic Laplacian on a geometrically finite hyperbolic surface, when the corresponding magnetic field is infinite at the boundary at infinity. We prove that the counting function of the eigenvalues has a particular asymptotic…

In this paper, the notion of hyperbolic ellipsoids in hyperbolic space is introduced. Using a natural orthogonal projection from hyperbolic space to Euclidean space, we establish affine isoperimetric type inequalities for static convex…

We employ Chen's conformal invariant quantity [8, Theorem 1] in combination with the Chern-Gauss-Bonnet formulas to obtain expressions for the renormalized area of asymptotically minimal hypersurfaces in the $(2n+1)$-dimensional hyperbolic…

This paper generalizes D. Burago and S. Ivanov's work on filling volume minimality and boundary rigidity of almost real hyperbolic metrics. We show that regions with metrics close to a negatively curved symmetric metric are strict minimal…

A nonuniform Neumann boundary-value problem is considered for the Poisson equation in a thin $3D$ aneurysm-type domain that consists of thin curvilinear cylinders that are joined through an aneurysm of diameter $\mathcal{O}(\varepsilon).$ A…

We consider area minimizing $m$-dimensional currents $\mathrm{mod}(p)$ in complete $C^2$ Riemannian manifolds $\Sigma$ of dimension $m+1$. For odd moduli we prove that, away from a closed rectifiable set of codimension $2$, the current in…

In this paper, we describe the intersection between geodesic and conformal currents on closed hyperbolic three-manifolds. We use this to prove some sharp bounds which involve the Liouville entropy of a negatively curved metric, the minimal…

In this paper we extend to $UCW$-hyperbolic spaces the quantitative asymptotic regularity results for the alternating Halpern-Mann iteration obtained by Dinis and the second author for CAT(0) spaces. These results are new even for uniformly…

We consider the three-dimensional incompressible magnetohydrodynamics (MHD) equations in a bounded domain with small volume and free moving surface boundary. We establish a priori estimate for solutions with minimal regularity assumptions…