In this paper we prove that Urysohn univeral space is hyperconvex. We also examine the Gromov hyperbolicity and hyperconvexity of metric spaces. Using fourpoint property, we give a proof of the fact that hyperconvex hull of a δ-Gromov hyperbolic space is also δ-Gromov hyperbolic.

The unit ball B is shown to be Gromov hyperbolic with respect to the Ferrand metric λBn and the modulus metric μBn , and dimension dependent upper bounds for the Gromov delta are obtained. In the two-dimensional case Gromov hyperbolicity is proved for all simply connected domains G. For λG also the case G = R n \ {0} is studied.

We make a precise mathematical statement of the conjecture that Gromov-Witten theory on an orbifold should be equivalent to Gromov-Witten theory on a crepant resolution (should one exist.) We prove the conjecture for the equivariant Gromov-Witten theories of Symn C and Hilbn C.

Given a holomorphic vector bundle E over a compact Kähler manifold X, one defines twisted Gromov-Witten invariants of X to be intersection numbers in moduli spaces of stable maps f : Σ → X with the cap product of the virtual fundamental class and a chosen multiplicative invertible characteristic class of the virtual vector bundle H0(Σ, f∗E) H1(Σ, f∗E). Using the formalism of quantized quadratic...

A quantized metric space is a matrix order unit space equipped with an operator space version of Rieffel’s Lip-norm. We develop for quantized metric spaces an operator space version of quantum Gromov-Hausdorff distance. We show that two quantized metric spaces are completely isometric if and only if their quantized Gromov-Hausdorff distance is zero. We establish a completeness theorem. As appli...

This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These GromovWitten type invariants depend on a Calabi-Yau A∞ category, which plays the role of the target in ordinary Gromov-Witten theory. When the Fukaya category of a compact symplectic manifold X is used, it is shown, under certain assumptions, that the u...

In the approach to Gromov–Witten theory developed by Givental, genus-zero Gromov–Witten invariants of a manifold X are encoded by a Lagrangian cone in a certain infinite-dimensional symplectic vector space. We give a construction of this cone, in the spirit of S-equivariant Floer theory, in terms of S-equivariant Gromov–Witten theory of X × P. This gives a conceptual understanding of the “dilat...

In this paper, the notion of almost S^{*}-compactness in L-topologicalspaces is introduced following Shi’s definition of S^{*}-compactness. The propertiesof this notion are studied and the relationship between it and otherdefinitions of almost compactness are discussed. Several characterizations ofalmost S^{*}-compactness are also presented.

in current study, seven organic fertilizers including; leaf mold (lm), rice husk (rh), manure, spent mushroom compost (smc), mixture of lm, rh and smc (m 1), mixture of lm, rh and manure (m 2) with the ratio of 1:1:1 and control (no fertilizer) along with some levels of soil compactness comprising roller weights of 36, 56, 76 kilogram were used. treatments were applied in a strip plot design wi...