Isoperimetric Inequalities for Minimal Submanifolds in Riemannian Manifolds: A Counterexample in Higher Codimension

For compact Riemannian manifolds with convex boundary, B.White proved the following alternative: Either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small singular set. There is the natural question if a similar result is true for submanifolds of higher codimension. Specifically, B.White asked if the non-existence of an isoperimetric inequality for k-varifolds implies the existence of a nonzero, stationary, integral k-varifold. We present examples showing that this is not true in codimension greater than two. The key step is the construction of a Riemannian metric on the closed four-dimensional ball B with the following properties: (1) B has strictly convex boundary. (2) There exists a complete nonconstant geodesic. (3) There does not exist a closed geodesic in B.Comment: 11 pages, We changed the title and added a section that exhibits the relation between our example and the question posed by Brian White concerning isoperimetric inequalities for minimal submanifold

Domestic Rivalry and Export Performance: Theory and Evidence from International Airline Markets

The much-studied relationship between domestic rivalry and export performance consists of those supporting a national-champion rationale, and those supporting a rivalry rationale. While the empirical literature generally supports the positive effects of domestic rivalry, the national-champion rationale actually rests on firmer theoretical ground. We address this inconsistency by providing a theoretical framework that illustrates three paths via which domestic rivalry translates into enhanced international exports. Furthermore, empirical tests on the world airline industry elicit the existence of one particular path - an enhanced firm performance effect - that connects domestic rivalry with improved international exports

Quantum dots in magnetic fields: thermal response of broken symmetry phases

We investigate the thermal properties of circular semiconductor quantum dots in high magnetic fields using finite temperature Hartree-Fock techniques. We demonstrate that for a given magnetic field strength quantum dots undergo various shape phase transitions as a function of temperature, and we outline possible observable consequences.Comment: In Press, Phys. Rev. B (2001

Cluster Masses Accounting for Structure along the Line of Sight

Weak gravitational lensing of background galaxies by foreground clusters offers an excellent opportunity to measure cluster masses directly without using gas as a probe. One source of noise which seems difficult to avoid is large scale structure along the line of sight. Here I show that, by using standard map-making techniques, one can minimize the deleterious effects of this noise. The resulting uncertainties on cluster masses are significantly smaller than when large scale structure is not properly accounted for, although still larger than if it was absent altogether.Comment: 5 pages, 5 figure

On uniqueness of tangent cones for Einstein manifolds

We show that for any Ricci-flat manifold with Euclidean volume growth the tangent cone at infinity is unique if one tangent cone has a smooth cross-section. Similarly, for any noncollapsing limit of Einstein manifolds with uniformly bounded Einstein constants, we show that local tangent cones are unique if one tangent cone has a smooth cross-section

The ‘spirit of sport’, WADAs code review, and the search for an overlapping consensus

In this paper, we argue for the recognition that anti-doping is in itself first and foremost an ethical position. The current World Anti-doping Code formulation of ‘the spirit of sport’ is an acknowledgement of this point and a counterweight against scientific and technicist understandings of the nature of anti-doping itself. We critically review the Code formulations on ‘the spirit of sport’. Based on a theoretical background of various approaches to normative agreement and consensus in a setting of diversity of ‘comprehensive views’, we argue for revision of the Code. Specifically, we argue for a re-formulation of ‘the spirit of sport’ in terms of athlete protection and the preservation of the integrity of sporting competition that could meet requirements on an overlapping consensus among all WADA stakeholders. This is not just a matter of formality and Code acceptance. An overlapping consensus is not a mere modus vivendi but a normative consensus based on fair, honest, and transparent discourse in which participants deliberate in a setting of mutual respect and trust, and of ‘decency’, which is a basis for a consensus that cultivates authentic stakeholder commitment

CMB-Cluster Lensing

Clusters of galaxies are powerful cosmological probes, particularly if their masses can be determined. One possibility for mass determination is to study the cosmic microwave background (CMB) on small angular scales and observe deviations from a pure gradient due to lensing of massive clusters. I show that, neglecting contamination, this technique has the power to determine cluster masses very accurately, in agreement with estimates by Seljak and Zaldarriaga (1999). However, the intrinsic small scale structure of the CMB significantly degrades this power. The resulting mass constraints are useless unless one imposes a prior on the concentration parameter c. With even a modest prior on c, an ambitious CMB experiment (0.5' resolution and 1 microK per pixel) could determine masses of high redshift (z>0.5) clusters with ~ 30% accuracy.Comment: 17 pages, 10 figure

Understanding young people's citizenship learning in everyday life: The role of contexts, relationships and dispositions

In this article we present insights from research which has sought to deepen understanding of the ways in which young people (13-21) learn democratic citizenship through their participation in a range of different formal and informal practices and communities. Based on the research, we suggest that such understanding should focus on the interplay between contexts for action, relationships within and across contexts, and the dispositions that young people bring to such contexts and relationships. In the first part of the paper we show how and why we have broadened the narrow parameters of the existing citizenship discourse with its focus on political socialisation to encompass a more wide-ranging conception of citizenship learning which is not just focused on school or the curriculum. In the second part of the paper we describe our research and present two exemplar case studies of young people who formed part of the project. In the third part we present our insights about the nature and character of citizenship learning that we have been able to draw from our research. In the concluding section we highlight those dimensions of citizenship learning that would have remained invisible had we focused exclusively on schools and the curriculum. In this way we demonstrate the potential of the approach to understanding citizenship learning that we have adopted

Cosmological parameters from SDSS and WMAP

We measure cosmological parameters using the three-dimensional power spectrum P(k) from over 200,000 galaxies in the Sloan Digital Sky Survey (SDSS) in combination with WMAP and other data. Our results are consistent with a ``vanilla'' flat adiabatic Lambda-CDM model without tilt (n=1), running tilt, tensor modes or massive neutrinos. Adding SDSS information more than halves the WMAP-only error bars on some parameters, tightening 1 sigma constraints on the Hubble parameter from h~0.74+0.18-0.07 to h~0.70+0.04-0.03, on the matter density from Omega_m~0.25+/-0.10 to Omega_m~0.30+/-0.04 (1 sigma) and on neutrino masses from <11 eV to <0.6 eV (95%). SDSS helps even more when dropping prior assumptions about curvature, neutrinos, tensor modes and the equation of state. Our results are in substantial agreement with the joint analysis of WMAP and the 2dF Galaxy Redshift Survey, which is an impressive consistency check with independent redshift survey data and analysis techniques. In this paper, we place particular emphasis on clarifying the physical origin of the constraints, i.e., what we do and do not know when using different data sets and prior assumptions. For instance, dropping the assumption that space is perfectly flat, the WMAP-only constraint on the measured age of the Universe tightens from t0~16.3+2.3-1.8 Gyr to t0~14.1+1.0-0.9 Gyr by adding SDSS and SN Ia data. Including tensors, running tilt, neutrino mass and equation of state in the list of free parameters, many constraints are still quite weak, but future cosmological measurements from SDSS and other sources should allow these to be substantially tightened.Comment: Minor revisions to match accepted PRD version. SDSS data and ppt figures available at http://www.hep.upenn.edu/~max/sdsspars.htm