293 research outputs found
Vafa-Witten Estimates for Compact Symmetric Spaces
We give an optimal upper bound for the first eigenvalue of the untwisted
Dirac operator on a compact symmetric space G/H with rk G-rk H\le 1 with
respect to arbitrary Riemannian metrics. We also prove a rigidity statement.Comment: LaTeX, 11 pages. V2: Rigidity statement added, minor changes. To
appea
The Dirac operator on untrapped surfaces
We establish a sharp extrinsic lower bound for the first eigenvalue of the
Dirac operator of an untrapped surface in initial data sets without apparent
horizon in terms of the norm of its mean curvature vector. The equality case
leads to rigidity results for the constraint equations with spherical boundary
as well as uniqueness results for constant mean curvature surfaces in Minkowski
space.Comment: 16 page
On a spin conformal invariant on manifolds with boundary
On a n-dimensional connected compact manifold with non-empty boundary
equipped with a Riemannian metric, a spin structure and a chirality operator,
we study some properties of a spin conformal invariant defined from the first
eigenvalue of the Dirac operator under the chiral bag boundary condition. More
precisely, we show that we can derive a spinorial analogue of Aubin's
inequality.Comment: 26 page
Rigidity of compact Riemannian spin Manifolds with Boundary
In this article, we prove new rigidity results for compact Riemannian spin
manifolds with boundary whose scalar curvature is bounded from below by a
non-positive constant. In particular, we obtain generalizations of a result of
Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake
\cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et
rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy
Currents and Superpotentials in classical gauge invariant theories I. Local results with applications to Perfect Fluids and General Relativity
E. Noether's general analysis of conservation laws has to be completed in a
Lagrangian theory with local gauge invariance. Bulk charges are replaced by
fluxes of superpotentials. Gauge invariant bulk charges may subsist when
distinguished one-dimensional subgroups are present. As a first illustration we
propose a new {\it Affine action} that reduces to General Relativity upon gauge
fixing the dilatation (Weyl 1918 like) part of the connection and elimination
of auxiliary fields. It allows a comparison of most gravity superpotentials and
we discuss their selection by the choice of boundary conditions. A second and
independent application is a geometrical reinterpretation of the convection of
vorticity in barotropic nonviscous fluids. We identify the one-dimensional
subgroups responsible for the bulk charges and thus propose an impulsive
forcing for creating or destroying selectively helicity. This is an example of
a new and general Forcing Rule.Comment: 64 pages, LaTeX. Version 2 has two more references and one misprint
corrected. Accepted in Classical and Quantum Gravit
K\"{a}hler-Einstein metrics on strictly pseudoconvex domains
The metrics of S. Y. Cheng and S.-T. Yau are considered on a strictly
pseudoconvex domains in a complex manifold. Such a manifold carries a complete
K\"{a}hler-Einstein metric if and only if its canonical bundle is positive. We
consider the restricted case in which the CR structure on is
normal. In this case M must be a domain in a resolution of the Sasaki cone over
. We give a condition on a normal CR manifold which it cannot
satisfy if it is a CR infinity of a K\"{a}hler-Einstein manifold. We are able
to mostly determine those normal CR 3-manifolds which can be CR infinities.
Many examples are given of K\"{a}hler-Einstein strictly pseudoconvex manifolds
on bundles and resolutions.Comment: 30 pages, 1 figure, couple corrections, improved a couple example
Deformations of the hemisphere that increase scalar curvature
Consider a compact Riemannian manifold M of dimension n whose boundary
\partial M is totally geodesic and is isometric to the standard sphere S^{n-1}.
A natural conjecture of Min-Oo asserts that if the scalar curvature of M is at
least n(n-1), then M is isometric to the hemisphere S_+^n equipped with its
standard metric. This conjecture is inspired by the positive mass theorem in
general relativity, and has been verified in many special cases. In this paper,
we construct counterexamples to Min-Oo's conjecture in dimension n \geq 3.Comment: Revised version, to appear in Invent. Mat
Exploring concepts of health with male prisoners in three category-C English prisons
Lay understandings of health and illness have a well established track record and a plethora of research now exists which has examined these issues. However, there is a dearth of research which has examined the perspectives of those who are imprisoned. This paper attempts to address this research gap. The paper is timely given that calls have been made to examine lay perspectives in different geographical locations and a need to re-examine health promotion approaches in prison settings. Qualitative data from thirty-six male sentenced prisoners from three prisons in England were collected. The data was analysed in accordance with Attride-Stirling's (2001) thematic network approach. Although the men's perceptions of health were broadly similar to the general population, some interesting findings emerged which were directly related to prison life and its associated structures. These included access to the outdoors and time out of their prison cell, as well as maintaining relationships with family members through visits. The paper proposes that prisoners' lay views should be given higher priority given that prison health has traditionally been associated with medical treatment and the bio-medical paradigm more generally. It also suggests that in order to fulfil the World Health Organization's (WHO) vision of viewing prisons as health promoting settings, lay views should be recognised to shape future health promotion policy and practice
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