Let $${{\cal T}_K}\left( D \right)$$ be the class of K-quasiconformal automorphisms a domain ⊂ ℝn with identity boundary values. Teichmüller’s problem is to determine how far given point x ∈ can mapped under mapping $$f \in {{\cal . We estimate this distance between and f(x) from above by using two different metrics, ratio metric quasihyperbolic metric. study for Gromov hyperbolic domains in va...

For a contractive iterated function system (IFS), it is known that there natural hyperbolic graph structure (augmented tree) on the symbolic space of IFS reflects relationship among neighboring cells, and its boundary with Gromov metric Hölder equivalent to attractor K [14], [26], [28]. This setup was taken up study probabilistic potential theory [21], [20], bi-Lipschitz equivalence [29]. In th...

We construct a version of relative Gromov-Witten theory with expanded degenerations in the normal crossings setting and establish degeneration formula for resulting invariants. Given simple pair $(X,D)$, we virtually smooth proper moduli spaces curves $X$ prescribed boundary conditions along $D$. Each point such space parameterizes maps from nodal to that are dimensionally transverse strata. us...

Abstract Gromov–Wasserstein distances were proposed a few years ago to compare distributions which do not lie in the same space. In particular, they offer an interesting alternative Wasserstein for comparing probability measures living on Euclidean spaces of different dimensions. We focus distance with ground cost defined as squared distance, and we study form optimal plan between Gaussian dist...

— We discuss how the geometry of D2-D0 branes may be related to Gromov-Witten theory of Calabi-Yau threefolds.

We compare the random group model of Gromov and the model of generic groups of Arzhantseva and Ol’shanskii.

We recall the construction of the Gromov–Wasserstein distance and concentrate on quantitative aspects of the definition.