76,404 research outputs found
Improved eigenvalue bounds for Schr\"odinger operators with slowly decaying potentials
We extend a result of Davies and Nath on the location of eigenvalues of
Schr\"odinger operators with slowly decaying complex-valued potentials to
higher dimensions. In this context, we also discuss various examples related to
the Laptev--Safronov conjecture.Comment: Some typos correcte
Spectral theory of a mathematical model in Quantum Field Theory for any spin
In this paper we use the formalism of S.Weinberg in order to construct a
mathematical model based on the weak decay of hadrons and nuclei. In particular
we consider a model which generalizes the weak decay of the nucleus of the
cobalt. We associate with this model a Hamiltonian with cutoffs in a Fock
space. The Hamiltonian is self-adjoint and has an unique ground state. By using
the commutator theory we get a limiting absorption principle from which we
deduce that the spectrum of the Hamiltonian is absolutely continuous above the
energy of the ground state and below the first threshold.Comment: A subsection revise
Bounds on primitives of differential forms and cofilling inequalities
We prove that on a Riemannian manifold, a smooth differential form has a
primitive with a given (functional) upper bound provided the necessary weighted
isoperimetric inequalities implied by Stokes are satisfied. We apply this to
prove a comparison predicted by Gromov between the cofilling function and the
filling area.Comment: The new features of the main result are its sharpness and the fact
that the manifold is not assumed have bounded geometry, nor even to be
complete. This paper corresponds to a part of a talk given in January 2004 in
Haifa, at a workshop in memory of Robert Brooks. The other part, which is the
"translation" in the framework of geometric group theory, will soon be
deposited on arxi
Dual elliptic structures on CP2
We consider an almost complex structure J on CP2, or more generally an
elliptic structure E which is tamed by the standard symplectic structure. An
E-curve is a surface tangent to E (this generalizes the notion of
J(holomorphic)-curve), and an E-line is an E-curve of degree 1. We prove that
the space of E-lines is again a CP2 with a tame elliptic structure E^*, and
that each E-curve has an associated dual E^*-curve. This implies that the
E-curves, and in particular the J-curves, satisfy the Pl\"ucker formulas, which
restricts their possible sets of singularities.Comment: 18 pages The only difference with the first version is the mention of
the thesis of Benjamin MacKay ("Duality and integrable systems of
pseudoholomorphic curves", Duke University, 1999), which I did not know at
the time, and which contains a large part of the results of my pape
Geometric descriptions of polygon and chain spaces
We give a few simple methods to geometically describe some polygon and
chain-spaces in R^d. They are strong enough to give tables of m-gons and
m-chains when m <= 6
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