Related papers: Embedding of Higson compactification into the prod…

The standard conformal compactification of Euclidean space is the round sphere. We use conformal geodesics to give an elementary proof that this is the only possible conformal compactification.

As in the case of the associahedron and cyclohedron, the permutohedron can also be defined as an appropriate compactification of a configuration space of points on an interval or on a circle. The construction of the compactification endows…

For a convergent series with positive terms, we prove that the $\ell^\infty$ product space of bounded subspaces of the Gromov-Hausdorff space can be isometrically embedded into the Gromov-Hausdorff space, where each subspace consists of…

We find a compactification of the $\mathrm{SO}_{0}(2,3)$-Hitchin component by studying the degeneration of the induced metric on the unique equivariant maximal surface in the 4-dimensional pseudo-hyperbolic space $\mathbb{H}^{2,2}$. In the…

We show that in dimensions $>1$ the cohomology groups of the Higson compactification of the hyperbolic space $\H^n$ with respect to the $C_0$ coarse structure are trivial. Also we prove that the cohomology groups of the Higson…

We obtain a compact Sobolev embedding for $H$-invariant functions in compact metric-measure spaces, where $H$ is a subgroup of the measure preserving bijections. In Riemannian manifolds, $H$ is a subgroup of the volume preserving…

On a flat manifold, M. Kontsevich's formality quasi-isomorphism is compatible with cup-products on tangent cohomology spaces, in the sense that its derivative at any formal Poisson 2-tensor induces an isomorphism of graded commutative…

A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid immersed in a smooth manifold produces a closed current (known as generalized…

We consider isometric immersions of complete connected Riemannian manifolds into space forms of nonzero constant curvature. We prove that if such an immersion is compact and has semi-definite second fundamental form, then it is an embedding…

The purpose of this article is to characterize the quasi-isometry type of a proper metric space via the Banach algebra of Higson functions on it.

The characteristic feature of the adeles is that they involve localizations of products (or equivalently restricted products of localizations). The point of this paper is to introduce an adelic style cohomological invariant of a partially…

We define generalized currents associated with immersions of abstract oriented solenoids with a transversal measure. We realize geometrically the full real homology of a compact manifold with these generalized currents, and more precisely…

We introduce the \emph{parameter-geometrization} to the Hitchin system, a paradigm embedding deformation parameters into geometry via the coupled Hitchin-He equations on a surface with boundary. A boundary term couples a second Higgs field…

Let (X,\omega) be a compact K\"ahler manifold. As discovered in the late 1980s by Mabuchi, the set H_0 of K\"ahler forms cohomologous to \omega has the natural structure of an infinite dimensional Riemannian manifold. We address the…

Pulling back complex structures along a branched covering induces a holomorphic isometric embedding of Teichm\"uller spaces. We show that for dimension at least $2$, all isometric embeddings arise from branched coverings. This generalizes a…

We prove that for any Riemannian metric $g$ on a closed orientable surface $\Sigma$ and any spacelike embedding $f:\Sigma \rightarrow M$ in a pseudo-Riemannian manifold $(M,h)$, the embedding $f$ can be $C^{0}$-approximated by a smooth…

After 1-point compactification, the collection of all unordered configuration spaces of a manifold admits a commutative multiplication by superposition of configurations. We explain a simple (derived) presentation for this commutative…

We endow the space of projective filling geodesic currents on a closed hyperbolic surface with a natural asymmetric metric extending Thurston's asymmetric metric on Teichm\"uller space, as well as analogous metrics arising from Hitchin…

The aim of this paper is to introduce the sublinear Higson corona and show that the sublinear Higson corona of Euclidean cone of P and X is decomposed into the product of P and that of X. Here P is a compact metric space and X is unbounded…

We prove a compactness theorem for embedded measured hyperbolic Riemann surface laminations in a compact almost complex manifold $(X, J)$. To prove compactness result, we show that there is a suitable topology on the space of measured…