Related papers: Gromov Ellipticity and subellipticity

We generalise the notion of separable equivalence, originally presented by Linckelmann (2011), to an equivalence relation on additive categories. We use this generalisation to show that from an initial equivalence between two algebras we…

We prove an analogue in Arakelov geometry of the Grothendieck-Riemann-Roch theorem.

We define a new equivalence between algebras for n-globular operads which is suggested in [Cottrell 2015], and show that it is a generalization of ordinary equivalence between categories.

In this paper, we develop a new index theory for manifolds with polyhedral boundary. As an application, we prove Gromov's dihedral extremality conjecture regarding comparisons of scalar curvatures, mean curvatures and dihedral angles…

The aim of this paper is to clarify the relationship between Gromov-hyperbolicity and amenability for planar maps.

We show that every projective Oka manifold is elliptic in the sense of Gromov. This gives an affirmative answer to a long-standing open question.

In this paper, we study certain applications of sphericalization in Gromov hyperbolic metric spaces. We first show that the doubling property regarding two classes of metrics on the Gromov boundary of hyperbolic spaces are coincided. Next,…

Let $n,m\ge 1$, $\alpha\in(0,1)$, and $\beta\ge 0$. For the Grushin-type operator \[ L=-\nabla_x\!\cdot\!\bigl(|x|^{2\alpha}\nabla_x\bigr)+|x|^{2\beta}\Delta_y \qquad \text{on } \mathbb R^n\times \mathbb R^m, \] we prove the isoperimetric…

We prove that the Gromov width of coadjoint orbits of the symplectic group is at least equal to the upper bound known from the works of Zoghi and Caviedes. This establishes the actual Gromov width. Our work relies on a toric degeneration of…

We present an elliptic version of Selberg's integral formula.

We define orbifold elliptic genus for general orbifolds which generalizes the definition of Borisov and Libgober, and prove their rigidity property.

We introduce a notion of elliptic differential graded Lie algebra. The class of elliptic algebras contains such examples as the algebra of differential forms with values in endomorphisms of a flat vector bundle over a compact manifold, etc.…

We give a cohomological characterization of Gromov relative hyperbolicity. As an application we prove a converse to the combination theorem for graphs of relatively hyperbolic groups given in a previous paper of the first author. We build…

We give an explicit formula for the Gromov width for a class of symplectic toric manifolds constructed from simple graphs. As a corollary, we show a version of non-squeezing theorem with respect to the inclusion of connected graphs.

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

The paper is essentially a continuation of B.Plotkin, G.Zhitomirski, "Some logical invariants of algebras and logical relations between algebras", St.Peterburg Math. J., {19:5}, (2008) 859 -- 879, whose main notion is that of…

In the variety of all linear algebras over the infinite field the difference between geometric and automorphic equivalence of algebras can be big.

We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…

This note collects a number of standard statements in Riemannian geometry and in Sobolev-space theory that play a prominent role in analytic approaches to symplectic topology. These include relations between connections and complex…

We develop a technique to obtain new symmetrization inequalities that provide a unified framework to study Sobolev inequalities, concentration inequalities and sharp integrability of solutions of elliptic equations