Concentration-compactness and finite-time singularities for Chen's flow

Chen's flow is a fourth-order curvature flow motivated by the spectral decomposition of immersions, a program classically pushed by B.-Y. Chen since the 1970s. In curvature flow terms the flow sits at the critical level of scaling together with the most popular extrinsic fourth-order curvature flow, the Willmore and surface diffusion flows. Unlike them however the famous Chen conjecture indicates that there should be no stationary nonminimal data, and so in particular the flow should drive all closed submanifolds to singularities. We investigate this idea, proving that (1) closed data becomes extinct in finite time in all dimensions and for any codimension; (2) singularities are characterised by concentration of curvature in $L^n$ for intrinsic dimension $n \in \{2,4\}$ and any codimension (a Lifespan Theorem); and (3) for $n = 2$ and in one codimension only, there exists an explicit small constant $\varepsilon_2$ such that if the $L^2$ norm of the tracefree curvature is initially smaller than $\varepsilon_2$, the flow remains smooth until it shrinks to a point, and that the blowup of that point is an embedded smooth round sphere.Comment: 48 page

How a professionals slash writer disrupts readers' expectations

Professionals fandom is a fertile ground for AU stories. At face value, Rhiannon's The Larton Chronicles is a pleasant, cozy AU that bears only a token resemblance to the show that inspired it. On closer examination, though, it disrupts a number of the themes that thread through The Professionals, including those of sexuality, race, and class

Mass Shootings and the Media: How Race and Ethnicity Influence Media Coverage

Topics related to crime and the criminal justice system comprise a majority of topics discussed in the media. This study explores how media coverage of mass shootings varies based on the racial or ethnic identity of the shooter. Topics examined include popular beliefs and misconceptions about the race of mass murderers, the role mass media plays in influencing public perceptions about race and crime related topics, and the alarming rate at which the public recognizes and accepts the media as a reliable source of information when official data sources provide a much different picture. Further analysis of the Columbine High School massacre and Virginia Tech shooting provides a more targeted and detailed examination of how the media dealt with the issue of race when reporting on these two shootings. Additional research focusing on a larger selection of mass shootings is needed to provide a more comprehensive understanding of the problem in its entirety. Regardless, the mass media’s representation of a shooter’s race and ethnicity has serious policy implications for the criminal justice system and public intergroup relations, indicating that extensive changes in how the media reports information surrounding these events are required

Analysis and Recommendations for the Property Tax on Motor Vehicles in Georgia

This report discusses the economic effects, including revenue effects, of eliminating or reducing the state property tax in motor vehicles. FRC Report 14

Do the poor need nutrition education? Some methodogical issues and suggestive evidence from Kinshasa, Zaire

African Studies Center Working Paper No. 2INTRODUCTION: It is frequently asserted that the diets of poor urban households in Africa and elsewhere are not nutritionally optimal, The composition of family food purchases is thought to be quite inefficient in many cases, reflecting the nutritional ignorance of the purchasers. At the same time, intrafamilial allocation of available foodstuffs is often seen as irrational in the sense that adult males, the least nutritionally vulnerable group, are given preference in feeding. [TRUNCATED

State Tax Incentives for Research and Development Activities:A Review of State Practices - Brief

This report documents state tax incentives offered around the country designed to encourage state level R&D activity.This report also simulates the effect of various credit components in the value of the credit. FRC Brief 13

Why I Teach

Thoughts about teaching by Linfield College facult