Degenerating Kähler–Einstein cones, locally symmetric cusps, and the Tian–Yau metric

Metric compacti cations of locally symmetric spaces

We introduce hyperbolic and asymptotic compactiications of metric spaces and apply them to locally symmetric spaces ?nX. We show that the reductive Borel{Serre compactiication ?nX RBS is hyperbolic and, as a corollary, get a result of Borel, and Kobayashi{Ochiai that the Baily{Borel compactiication ?nX BB is hyperbolic. We prove that the hyperbolic reduction of the toroidal compactiications ?nX...

Conformally Converting Cusps to Cones

Conformal deformations of hyperbolic surfaces with conical singularities are shown to be real-analytic. The first nontrivial term in the power series expansion around a cusped surface is shown to be a multiple of the Eisenstein series E2.

Bornological Completion of Locally Convex Cones

In this paper, firstly, we obtain some new results about bornological convergence in locally convex cones (which was studied in [1]) and then we introduce the concept of bornological completion for locally convex cones. Also, we prove that the completion of a bornological locally convex cone is bornological. We illustrate the main result by an example.

Some Results on Boundedness in Locally Convex Cones

Egoroff Theorem for Operator-Valued Measures in Locally Convex Cones

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...