In the context of optimal transport (OT) methods, subspace detour approach was recently proposed by Muzellec and Cuturi. It consists first finding an plan between measures projected on a wisely chosen then completing it in nearly whole space. The contribution this paper is to extend category methods Gromov–Wasserstein problem, which particular type OT distance involving specific geometry each d...

It is well known that, when endowed with the Gromov-Hausdorff distance dGH, collection M of all isometry classes compact metric spaces a complete and separable space. also that (M,dGH) geodesic space, but there no structural characterization geodesics in M. In this paper we provide two characterizations We call γ:[0,1]→M Hausdorff-realizable if exists space Z containing isometric copies γ(t) fo...

In this paper we prove: if the complete Kähler-Einstein metric on a bounded convex domain (with no boundary regularity assumptions) is Gromov hyperbolic, then ?¯-Neumann problem satisfies subelliptic estimate. This accomplished by constructing plurisubharmonic function whose Hessian grows at certain rate (which implies estimate work of Catlin and Straube). We also provide characterization hyper...

We show that the WDVV equations determine the genus zero Gromov–Witten invariants of the stack symmetric square of P 2 from the 3-point invariants and certain degree 0 invariants. These degree 0 invariants can be expressed in terms of hyperelliptic Hodge integrals that have been computed by Faber and Pandharipande [11]. A direct comparison with Graber's calculation [12] shows that the Gromov–Wi...

This paper considers the question of relative hyperbolicity of an Artin group with regard to the geometry of its associated Deligne complex. We prove that an Artin group is weakly hyperbolic relative to its finite (or spherical) type parabolic subgroups if and only if its Deligne complex is a Gromov hyperbolic space. For a 2-dimensional Artin group the Deligne complex is Gromov hyperbolic preci...