102,417 research outputs found
Kahler-Einstein metrics with edge singularities
This article considers the existence and regularity of Kahler-Einstein
metrics on a compact Kahler manifold with edge singularities with cone
angle along a smooth divisor . We prove existence of such
metrics with negative, zero and some positive cases for all cone angles
. The results in the positive case parallel those in the
smooth case. We also establish that solutions of this problem are
polyhomogeneous, i.e., have a complete asymptotic expansion with smooth
coefficients along for all .Comment: with an appendix by Chi Li and Yanir A. Rubinstein. Accepted by
Annals of Mat
Rearrangement Groups of Fractals
We construct rearrangement groups for edge replacement systems, an infinite
class of groups that generalize Richard Thompson's groups F, T, and V .
Rearrangement groups act by piecewise-defined homeomorphisms on many
self-similar topological spaces, among them the Vicsek fractal and many Julia
sets. We show that every rearrangement group acts properly on a locally finite
CAT(0) cubical complex, and we use this action to prove that certain
rearrangement groups are of type F infinity.Comment: 48 pages, 37 figure
Ramsey expansions of metrically homogeneous graphs
We discuss the Ramsey property, the existence of a stationary independence
relation and the coherent extension property for partial isometries (coherent
EPPA) for all classes of metrically homogeneous graphs from Cherlin's
catalogue, which is conjectured to include all such structures. We show that,
with the exception of tree-like graphs, all metric spaces in the catalogue have
precompact Ramsey expansions (or lifts) with the expansion property. With two
exceptions we can also characterise the existence of a stationary independence
relation and the coherent EPPA.
Our results can be seen as a new contribution to Ne\v{s}et\v{r}il's
classification programme of Ramsey classes and as empirical evidence of the
recent convergence in techniques employed to establish the Ramsey property, the
expansion (or lift or ordering) property, EPPA and the existence of a
stationary independence relation. At the heart of our proof is a canonical way
of completing edge-labelled graphs to metric spaces in Cherlin's classes. The
existence of such a "completion algorithm" then allows us to apply several
strong results in the areas that imply EPPA and respectively the Ramsey
property.
The main results have numerous corollaries on the automorphism groups of the
Fra\"iss\'e limits of the classes, such as amenability, unique ergodicity,
existence of universal minimal flows, ample generics, small index property,
21-Bergman property and Serre's property (FA).Comment: 57 pages, 14 figures. Extends results of arXiv:1706.00295. Minor
revisio
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