Related papers: Cone structure of $L^2$-Wasserstein spaces

The Urysohn space is a complete separable metric space, universal among separable metric spaces for extending finite partial isometries into it. We present an alternative construction of the Urysohn space which enables us to show that…

We give an exact mathematical construction of a spacelike order $<$, which is dual to the standard chronological order $\ll$ in the $n$-dimensional Minkowski space $M^n$, and we discuss its order-theoretic, geometrical as well as its…

We present some features of the smooth structure, and of the canonical stratification on the orbit space of a proper Lie groupoid. One of the main features is that of Morita invariance of these structures - it allows us to talk about the…

A notion of differentiability is being proposed for maps between Wasserstein spaces of order 2 of smooth, connected and complete Riemannian manifolds. Due to the nature of the tangent space construction on Wasserstein spaces, we only give a…

Let G be a complex reductive group and D a finite subset of a compact Riemann surface X. It was shown in [BJ] that the moduli space of G-characters of the complement of D in X has a natural Poisson structure. We show that the moduli space…

Optical (or Robinson) structures are one generalisation of four-dimensional shearfree congruences of null geodesics to higher dimensions. They are Lorentzian analogues of complex and CR structures. In this context, we extend the…

This paper is concerned with a covering problem of Euclidean space by a particular arrangement of cones that are not necessarily full and are allowed to overlap. The problem provides an equivalent geometric reformulation of the solvability…

We review part of the classical theory of curves and surfaces in $3$-dimensional Lorentz-Minkowski space. We focus in spacelike surfaces with constant mean curvature pointing the differences and similarities with the Euclidean space.

Wasserstein distances define a metric between probability measures on arbitrary metric spaces, including meta-measures (measures over measures). The resulting Wasserstein over Wasserstein (WoW) distance is a powerful, but computationally…

We investigate the complex geometry of D=10 pure spinor space. The K\"ahler structure and the corresponding metric giving rise to the desired Calabi-Yau property are determined, and an explicit covariant expression for the Laplacian is…

Let W -> A^2 be the universal Weierstrass family of cubic curves over C. For each N >= 2, we construct surfaces parametrizing the three standard kinds of level N structures on the smooth fibers of W. We then complete these surfaces to…

The Z-property of a linear map with respect to a cone is an extension of the notion of Z-matrices. In a recent paper of Orlitzky (see Corollary 6.2 in M. Orlitzky. Positive and $\mathbf{Z}$-operators on closed convex cones, Electron. J…

We study the structure of Busemann spaces with measures satisfying the measure contraction property (MCP). The main results are rigidity theorems and structure theorems under the assumption of geodesic completeness or non-collapse. The…

We first define a complex angle between two oriented spacelike planes in 4-dimensional Minkowski space, and then study the constant angle surfaces in that space, i.e. the oriented spacelike surfaces whose tangent planes form a constant…

In this article, examples of Zariski pairs $(B_1, B_2)$ satisfying the following condition are given: (i) $\deg B_1 = \deg B_2 = 7$. (ii) Irreducible components of $B_i$ $(i = 1, 2)$ are lines and conics. (iii) Singularities of $B_i$ $(i =…

Given a differential graded Lie algebra (dgla) L satisfying certain conditions, we construct Poisson structures on the gauge orbits of its set of Maurer-Cartan (MC) elements, termed Maurer-Cartan-Poisson (MCP) structures. They associate a…

Reflexive cones in Banach spaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the…

We show that warped cones over actions with spectral gaps do not embed coarsely into large classes of Banach spaces. In particular, there exist warped cones over actions of the free group that do not embed coarsely into $L_p$-spaces and…

We construct locally Lindel\"of scattered P-spaces (LLSP spaces, in short) with prescribed widths and heights under different set-theoretic assumptions. We prove that there is an LLSP space of width $\omega_1$ and height $\omega_2$ and that…

We classify hypersurfaces of the Minkowski space $\L^{n+1}$ that carry a totally geodesic foliation with complete leaves of codimension one. We prove that such a hypersurface is ruled, or a partial tube over a curve or contains a two or…