65,368 research outputs found
Combinatorial Quantum Field Theory and Gluing Formula for Determinants
We define the combinatorial Dirichlet-to-Neumann operator and establish a
gluing formula for determinants of discrete Laplacians using a combinatorial
Gaussian quantum field theory. In case of a diagonal inner product on cochains
we provide an explicit local expression for the discrete Dirichlet-to-Neumann
operator. We relate the gluing formula to the corresponding Mayer-Vietoris
formula by Burghelea, Friedlander and Kappeler for zeta-determinants of
analytic Laplacians, using the approximation theory of Dodziuk. Our argument
motivates existence of gluing formulas as a consequence of a gluing principle
on the discrete level.Comment: 26 pages, accepted for publication at Letters in Math. Physic
Numerical Brill-Lindquist initial data with a Schwarzschildean end at spatial infinity
We construct numerically time-symmetric initial data that are
Schwarzschildean at spatial infinity and Brill-Lindquist in the interior. The
transition between these two data sets takes place along a finite gluing region
equipped with an axisymmetric Brill wave metric. The construction is based on
an application of Corvino's gluing method using Brill waves due to Giulini and
Holzegel. Here, we use a gluing function that includes a simple angular
dependence. We also investigate the dependence of the ADM mass of our
construction on the details of the gluing procedure.Comment: 6 pages, 1 figure, 1 table. Conference proceedings for the Spanish
Relativity Meeting, Valencia 201
Gluing hyperconvex metric spaces
We investigate how to glue hyperconvex (or injective) metric spaces such that
the resulting space remains hyperconvex. We give two new criteria, saying that
on the one hand gluing along strongly convex subsets and on the other hand
gluing along externally hyperconvex subsets leads to hyperconvex spaces.
Furthermore, we show by an example that these two cases where gluing works are
opposed and cannot be combined.Comment: 11 page
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