Related papers: Asymptotically optimal designs on compact algebrai…

We investigate the class of geodesic metric discs satisfying a uniform quadratic isoperimetric inequality and uniform bounds on the length of the boundary circle. We show that the closure of this class as a subset of Gromov-Hausdorff space…

Given a point A in the real Grassmannian, it is well-known that one can construct a soliton solution u_A(x,y,t) to the KP equation. The contour plot of such a solution provides a tropical approximation to the solution when the variables x,…

Two compactifications of the space of holomorphic maps of fixed degree from a compact Riemann surface to a Grassmannian are studied. It is shown that the Uhlenbeck compactification has the structure of a projective scheme and is dominated…

We give some new explicit examples of putatively optimal projective spherical designs. i.e., ones for which there is numerical evidence that they are of minimal size. These form continuous families, and so have little apparent symmetry in…

We solve the classical problem of Plateau in every metric space which is $1$-complemented in an ultra-completion of itself. This includes all proper metric spaces as well as many locally non-compact metric spaces, in particular, all dual…

In this paper we prove the conjecture of Korevaar and Meyers: for each $N\ge c_dt^d$ there exists a spherical $t$-design in the sphere $S^d$ consisting of $N$ points, where $c_d$ is a constant depending only on $d$.

We study quaternionic Bott-Chern cohomology on compact hypercomplex manifolds and adapt some results from complex geometry to the quaternionic setting. For instance, we prove a criterion for the existence of HKT metrics on compact…

We classify isotopy classes of automorphisms (self-homeomorphisms) of 3-manifolds satisfying the Thurston Geometrization Conjecture. The classification is similar to the classification of automorphisms of surfaces developed by Nielsen and…

We continue the study of optimal chordal packings, with emphasis on packing subspaces of dimension greater than one. Following a principle outlined in a previous work, where the authors use maximal affine block designs and maximal sets of…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field. Criteria are given which characterize existence of a fine or coarse moduli space classifying, up to isomorphism, the representations of $\Lambda$ with fixed…

We give a geometric interpretation of the maximal Satake compactification of symmetric spaces $X=G/K$ of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable $G$-invariant Finsler metric on $X$. As…

The theory of designs is an important branch of combinatorial mathematics. It is well-known in the theory of designs that a finite subset of a sphere is a tight spherical 1-design if and only if it is a pair of antipodal points. On the…

We study the automorphisms of compact K\"ahler manifolds having slow dynamics. By adapting Gromov's classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that…

We study fractional Sobolev and Besov spaces on noncompact Riemannian manifolds with bounded geometry. Usually, these spaces are defined via geodesic normal coordinates which, depending on the problem at hand, may often not be the best…

We study partitions on three dimensional manifolds which minimize the total geodesic perimeter. We propose a relaxed framework based on a $\Gamma$-convergence result and we show some numerical results. We compare our results to those…

Under the definition of Ricci curvature bounded below for Alexandrov spaces introduced by Zhang-Zhu, we generalize a result by Colding that an n dimentional manifold with Ricci curvature greater or equal to n minus 1 and volume close to…

For an Alexandrov space (with curvature bounded below), we determine the maximal dimension of its isometry group and show that the space is isometric to a Riemannian manifold, provided the dimension of its isometry group is maximal. We also…

We analyse in all generality beyond Horndeski theories of shift symmetry in a static and spherically symmetric spacetime. By introducing four auxiliary functions, we write the field equations in a particularly compact form. We show that…

We investigate the approximation of Monge--Kantorovich problems on general compact metric spaces, showing that optimal values, plans and maps can be effectively approximated via a fully discrete method. First we approximate optimal values…

We develop new elements of harmonic analysis on the complex sphere on the basis of which Bernstein's, Jackson's and Kolmogorov's inequalities are established. We apply these results to get order sharp estimates of $m$-term approximations.…