7,177 research outputs found
On Counterfactuals and Contextuality
Counterfactual reasoning and contextuality is defined and critically
evaluated with regard to its nonempirical content. To this end, a uniqueness
property of states, explosion views and link observables are introduced. If
only a single context associated with a particular maximum set of observables
can be operationalized, then a context translation principle resolves
measurements of different contexts.Comment: 10 pages, presented at Foundations of Probability and Physics-3,
Vaexjoe University, Sweden, June 7-12, 200
Hamiltonian 2-forms in Kahler geometry, III Extremal metrics and stability
This paper concerns the explicit construction of extremal Kaehler metrics on
total spaces of projective bundles, which have been studied in many places. We
present a unified approach, motivated by the theory of hamiltonian 2-forms (as
introduced and studied in previous papers in the series) but this paper is
largely independent of that theory.
We obtain a characterization, on a large family of projective bundles, of
those `admissible' Kaehler classes (i.e., the ones compatible with the bundle
structure in a way we make precise) which contain an extremal Kaehler metric.
In many cases, such as on geometrically ruled surfaces, every Kaehler class is
admissible. In particular, our results complete the classification of extremal
Kaehler metrics on geometrically ruled surfaces, answering several
long-standing questions.
We also find that our characterization agrees with a notion of K-stability
for admissible Kaehler classes. Our examples and nonexistence results therefore
provide a fertile testing ground for the rapidly developing theory of stability
for projective varieties, and we discuss some of the ramifications. In
particular we obtain examples of projective varieties which are destabilized by
a non-algebraic degeneration.Comment: 40 pages, sequel to math.DG/0401320 and math.DG/0202280, but largely
self-contained; partially replaces and extends math.DG/050151
A new critical curve for a class of quasilinear elliptic systems
We study a class of systems of quasilinear differential inequalities
associated to weakly coercive differential operators and power reaction terms.
The main model cases are given by the -Laplacian operator as well as the
mean curvature operator in non parametric form. We prove that if the exponents
lie under a certain curve, then the system has only the trivial solution. These
results hold without any restriction provided the possible solutions are more
regular. The underlying framework is the classical Euclidean case as well as
the Carnot groups setting.Comment: 28 page
Universal graphs with forbidden subgraphs and algebraic closure
We apply model theoretic methods to the problem of existence of countable
universal graphs with finitely many forbidden connected subgraphs. We show that
to a large extent the question reduces to one of local finiteness of an
associated''algebraic closure'' operator. The main applications are new
examples of universal graphs with forbidden subgraphs and simplified treatments
of some previously known cases
The decomposition and classification of radiant affine 3-manifolds
An affine manifold is a manifold with torsion-free flat affine connection. A
geometric topologist's definition of an affine manifold is a manifold with an
atlas of charts to the affine space with affine transition functions; a radiant
affine manifold is an affine manifold with holonomy consisting of affine
transformations fixing a common fixed point. We decompose an orientable closed
radiant affine 3-manifold into radiant 2-convex affine manifolds and radiant
concave affine 3-manifolds along mutually disjoint totally geodesic tori or
Klein bottles using the convex and concave decomposition of real projective
-manifolds developed earlier. Then we decompose a 2-convex radiant affine
manifold into convex radiant affine manifolds and concave-cone affine
manifolds. To do this, we will obtain certain nice geometric objects in the
Kuiper completion of holonomy cover. The equivariance and local finiteness
property of the collection of such objects will show that their union covers a
compact submanifold of codimension zero, the complement of which is convex.
Finally, using the results of Barbot, we will show that a closed radiant affine
3-manifold admits a total cross section, confirming a conjecture of Carri\`ere,
and hence every radiant affine 3-manifold is homeomorphic to a Seifert fibered
space with trivial Euler number, or a virtual bundle over a circle with fiber
homeomorphic to a torus.Comment: Some notational mistakes fixed, and the appendix rewritte
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