2,880 research outputs found
The bisymplectomorphism group of a bounded symmetric domain
No full textIn a previous paper with A. Loi we introduced the so called symplectic duality between Hermitian symmetric spaces. Such duality consists in a bysimplectomorphism between an open and dense subset of a compact Hermitian symmetric space and its non-compact dual. The question about how many dualities does exists is directly related to the group of bi-symplectomorphism of a bounded symmetric domain of the complex euclidean space. In this paper we give a precise description of such group showing that its is a product of the isotropy group times the set of smooth function of the interval [0,1) to S^1. We study the group of bi-symplectomorphism of a bounded symmetric domai
Some remarks on Homogeneous Kaehler manifolds
No full textIn this paper we provide a positive answer to a conjecture due to Di Scala et al. (Asian J Math, 2012, Conjecture 1) claiming that a simply-connected homogeneous Kähler manifold M endowed with an integral Kähler form μ0ω, admits a holomorphic isometric immersion in the complex projective space, for a suitable >0μ0>0. This result has two corollaries which extend to homogeneous Kähler manifolds the results obtained by the authors Loi and Mossa (Geom Dedicata 161:119–128, 2012) and Mossa (J Geom Phys 86:492–496, 2014) for homogeneous bounded domains
Balanced metrics on Cartan and Cartan–Hartogs domains
No full textThis paper consists of two results dealing with balanced metrics (in Donaldson terminology) on noncompact complex manifolds. In the first one we describe all balanced metrics on Cartan domains. In the second one we show that the only Cartan-Hartogs domain which admits a balanced metric is the complex hyperbolic space. By combining these results with those obtained in Loi and Zedda (Mathematische Annalen, 2011) we also provide the first example of complete, Kähler-Einstein and projectively induced metric g such that αg is not balanced for all α > 0
Endowments, patience types, and uniqueness in two-good HARA utility economies
No full textThis paper establishes a link between endowments, patience types, and the parameters of the HARA Bernoulli utility function that ensure equilibrium uniqueness in an economy with two goods and two impatience types with additive separable preferences. We provide sufficient conditions that guarantee uniqueness of equilibrium for any possible value of γ in the HARA utility function γ 1−γ b+ a
γx 1−γ. The analysis contributes to the literature on uniqueness in pure exchange economies with two-goods and two agent types and extends the result in Loi and Matta (2022)
Symplectic duality of Symmetric Spaces
No full textWe show that between symmetric spaces of different types there exists a bi-symplectic map. We compute the duality map explicitely by using the theory of Jordan Algebra
Calabi's diastasis function for Hermitian symmetric spaces
No full textIn this paper we study the Calabi diastasis function of Hermitian symmetric spaces.
This allows us to prove that if a complete Hermitian
locally symmetric space (M, g) admits a Kaehler immersion into
a globally symmetric space (S, G)
then it is globally symmetric
and the immersion is injective.
Moreover, if (S, G) is symmetric
of a specified type
(Euclidean, noncompact, compact),
then (M, g) is of the same type.
We also give a characterization of
Hermitian globally
symmetric spaces in terms of their
diastasis function.
Finally, we apply our analysis to study the balanced metrics, introduced by Donaldson, in the case of locally
Hermitian symmetric spaces
Increasing complexity in structurally stable models: an application to a pure exchange economy
No full textA model M is defined (see Anderlini and Canning (2001) and Yu et al. (2009)) as a quadruple M = {Lambda, X, F, R}, where Lambda and X represent the parameter and actions spaces, respectively, F is a correspondence defining the feasible actions and R is a real-valued function which measures the degree of rationality of the feasible actions. We recall that structural stability means the continuity of the equilibrium set with respect to small perturbations of the parameters and that robustness to bounded rationality holds if small deviations from rationality imply small changes in the equilibrium set. In this paper we extend to a model (M) over bar = {(Lambda) over bar, (X) over bar, (F) over bar, (R) over bar}, where (Lambda) over bar is defined as the set of all compact subsets of A, (X) over bar = X, (F) over bar and (R) over bar are the feasibility and rationality correspondences which extend F and R, respectively. (M) over bar is more complex than M, since M is embedded into (M) over bar in a natural way. We show that the structural stability of A implies the structural stability of (M) over bar and that (M) over bar is robust to bounded rationality if (R) over bar is lower semi-continuous. This abstract characterization of complexity is important because it can be used to appraise the nontrivial issue of whether structural stability and robustness to bounded rationality are preserved when a structurally stable model M is extended to (M) over bar. By applying this abstract construction to a pure exchange economy, the result by Loi and Matta (2010), concerning the stability of the equilibrium set with respect to perturbations of endowments along a given path, is extended to perturbations of paths under bounded rationality. (C) 2015 Elsevier B.V. All rights reserved
A Laplace integral, the T-Y-Z expansion and Berezin's transform on a Kaehler manifold
No full textLet M be an n-dimensional complex manifold endowed with a C∞ Kähler metric g. We show that a certain Laplace-type integral Lm (x), when x varies in a sufficiently small open set U ⊂ M, has an asymptotic expansion Lm(x)= 1/mn ∑r≤0 m-rCr(f) (x), where Cr:C∞ (U) → C∞ (U) are smooth differential operators depending on the curvature of g and its covariant derivatives. As a consequence we furnish a different proof of Lu's theorem by computing the lower order terms of Tian-Yau-Zelditch expansion in terms of the operator Cj. Finally, we compute the differential operators Qj of the expansion Berm (f) = ∑r≤0 m-r Qr (f) of Berezin's transform in terms of the operators Cj
Regular quantizations of Kaehler manifolds and constant scalar curvature metrics
No full textIn this paper we prove that if a Ka ̈hler manifold (M, ω) admits a regular quantization then its scalar curvature is constant. Moreover, we apply this result to the two-dimensional complete Reinhardt domains in C2 to show that such domains admit a regular quantization iff they are biholomorphically isometric to the 2-ball in C2 endowed with the hyperbolic metric
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