Related papers: Bi-Halfspace and Convex Hull Theorems for Translat…

In the semiclassical domain the exponent of vortex quantum tunneling is dominated by a volume which is associated with the path the vortex line traces out during its escape from the metastable well. We explicitly show the influence of…

We show that any minimizing hypercone can be perturbed into one side to a properly embedded smooth minimizing hypersurface in the Euclidean space, and every viscosity mean convex cone admits a properly embedded smooth mean convex…

Liebmann's Theorem asserts that a compact, connected, convex surface with constant mean curvature (CMC) in the Euclidean space must be a totally umbilical sphere. In this article we extend Liebmann's result to hypersurfaces with boundary.…

This paper proves the following statement: If a convex body can form a three or fourfold translative tiling in the three-dimensional space, it must be a parallelohedron. In other words, it must be a parallelotope, a hexagonal prism, a…

We prove ``half-space" intersection properties in three settings: the hemisphere, half-geodesic balls in space forms, and certain subsets of Gaussian space. For instance, any two embedded minimal hypersurfaces in the sphere must intersect…

Translators can be regarded as submanifolds which satisfy the mean curvature flow equation when evolving by translations along a distinguished vector field of the ambient space. We study translators in Generalised Robertson-Walker…

This concise review aims to provide a summary of the most relevant recent experimental and theoretical results for solitons, i.e., self-trapped bound states of nonlinear waves, in two- and three-dimensional (2D and 3D) media. In comparison…

In this paper, we recall some general properties and theorems about Translating Solitons in Semi Riemannian Manifolds. Moreover, we investigate those which are invariant by the action of a Lie group of isometries of the ambient space, by…

In this paper, we construct the first analytic examples of (3+1)-dimensional self-gravitating regular cosmic tube solutions which are superconducting, free of curvature singularities and with non-trivial topological charge in the…

We define a moduli space of translation structures on the open topological disk with a basepoint and endow it with a locally-compact metrizable topology. We call this the immersive topology, because it is defined using the concept of…

We determine all asymptotically flat, supersymmetric and biaxisymmetric soliton and black hole solutions to five dimensional minimal supergravity. In particular, we show that the solution must be a multi-centred solution with a…

We develop a Helmholtz-like theorem for differential forms in Euclidean space $E_{n}$ using a uniqueness theorem similar to the one for vector fields. We then apply it to Riemannian manifolds, $R_{n}$, which, by virtue of the…

Symmetries of the physical world have guided formulation of fundamental laws, including relativistic quantum field theory and understanding of possible states of matter. Topological defects (TDs) often control the universal behavior of…

We prove a codimension reduction and congruence theorem for compact $n$-dimensional submanifolds of $\mathbb{S}^{n+p}$ that admit a mean convex isometric embedding into $\mathbb{S}^{n+1}_+$ using a Reilly type formula for space forms.

Let $(M,Q)$ be a compact, three dimensional manifold of strictly negative sectional curvature. Let $(\Sigma,P)$ be a compact, orientable surface of hyperbolic type (i.e. of genus at least two). Let $\theta:\pi_1(\Sigma,P)\to\pi_1(M,Q)$ be a…

We consider the mean curvature flow of compact convex surfaces in Euclidean $3$-space with free boundary lying on an arbitrary convex barrier surface with bounded geometry. When the initial surface is sufficiently convex, depending only on…

We study multiple tilings of 3-dimensional Euclidean space by a convex body. In a multiple tiling, a convex body $P$ is translated with a discrete multiset $\Lambda$ in such a way that each point of the space gets covered exactly $k$ times,…

Existence and uniqueness in Minkowski space of entire downward translating solitons with prescribed values at infinity for a scalar curvature flow equation. The radial case translates into an ordinary differential equation and the general…

Let $M$ be an $n$-dimensional smooth oriented complete embedded minimal hypersurface in $\mathbb{R}^{n+1}$ with Euclidean volume growth. We show that if the image under the Gauss map of $M$ avoids some neighborhood of a half-equator, then…

We prove that if a translating soliton can be expressed as the sum of two curves and one of these curves is planar, then the other curve is also planar and consequently the surface must be a plane or a grim reaper. We also investigate…