Related papers: Remarks on holomorphic isometric embeddings betwee…

In this article, we give multiple situations when having one or two geometrically distinct closed geodesics on a complete Riemannian cylinder $M\simeq S^1\times\mathbb{R}$ or a complete Riemannian plane $M\simeq\mathbb{R}^2$ leads to having…

Homotopy is an important feature of associative and Jordan algebraic structures: such structures always come in families whose members need not be isomorphic among other, but still share many important properties. One may regard homotopy as…

For smooth embeddings of an integral homology 3-sphere in the 6-sphere, we define an integer invariant in terms of their Seifert surfaces. Our invariant gives a bijection between the set of smooth isotopy classes of such embeddings and the…

We address various topologies (de Bruijn, chordal ring, generalized Petersen, meshes) in various ways ( isometric embedding, embedding up to scale, embedding up to a distance) in a hypercube or a half-hypercube. Example of obtained…

We study the homeomorphic extension of biholomorphisms between convex domains in $\mathbb C^d$ without boundary regularity and boundedness assumptions. Our approach relies on methods from coarse geometry, namely the correspondence between…

We study the complexity of holomorphic isometries and proper maps from the complex unit ball to type IV classical domains. We investigate on degree estimates of holomorphic isometries and holomorphic maps with minimum target dimension. We…

Let G be a reductive group over an algebraically closed field of characteristic p>0. We study properties of embeddings of spherical homogeneous G-spaces. We look at Frobenius splittings, canonical or by a (p-1)-th power, compatible with…

Let X be an arbitrary hyperbolic geodesic metric space and let G be a countable non-elementary weakly acylindrical group of isometries of X. We show that the second bounded cohomology group of G with real coefficients or with coefficients…

Motivated by spectral asymptotics for orbital integrals in a relative trace formula, we generalize a number of geometric properties of geodesics in the hyperbolic plane, to maximal flat submanifolds of symmetric spaces of non-compact type.

This paper is the last in a series of three papers which investigate pseudoholomorphic strips in the symplectisation of a three dimensional closed contact manifold with a mixed boundary condition. We will prove a compactness and an…

This writeup describes ongoing work on designing and testing a certain family of correspondences between compact metric spaces that we call \emph{embedding-projection correspondences} (EPCs). Of particular interest are EPCs between spheres…

Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev…

We prove a Runge theorem for and describe the homology of axially symmetric open subsets of H.

We study the problem of construction of explicit isometric embeddings of (pseudo)-Riemannian manifolds. We discuss the method which is based in the idea that the exterior symmetry of the embedded surface and the interior symmetry of the…

In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their…

The analysis of manifold valued data using embedding based methods is linked to the problem of finding suitable embeddings. In this paper we are interested in embeddings of quotient manifolds $\mathrm{SO}(3)/\mathcal{S}$ of the rotation…

In this article we show how holomorphic Riemannian geometry can be used to relate certain submanifolds in one pseudo-Riemannian space to submanifolds with corresponding geometric properties in other spaces. In order to do so, we shall first…

We classify maximal totally geodesic submanifolds in exceptional symmetric spaces up to isometry. Moreover, we introduce an invariant for certain totally geodesic embeddings of semisimple symmetric spaces, which we call the Dynkin index. We…

In the first part of this expository article, the most important constructions and classification results concerning totally geodesic submanifolds in Riemannian symmetric spaces are summarized. In the second part, I describe the results of…

In this paper, we study embeddings of uniform Roe algebras. Generally speaking, given metric spaces $X$ and $Y$, we are interested in which large scale geometric properties are stable under embedding of the uniform Roe algebra of $X$ into…