Inverse Mean Curvature Flow and the Stability of the Positive Mass Theorem and Riemannian Penrose Inequality Under L2L^2 Metric Convergence

We study the stability of the Positive Mass Theorem (PMT) and the Riemannian Penrose Inequality (RPI) in the case where a region of an asymptotically flat manifold $M^3$ can be foliated by a smooth solution of Inverse Mean Curvature Flow (IMCF) which is uniformly controlled. We consider a sequence of regions of asymptotically flat manifolds $U_T^i\subset M_i^3$, foliated by a smooth solution to IMCF which is uniformly controlled, and if $\partial U_T^i = \Sigma_0^i \cup \Sigma_T^i$ and $m_H(\Sigma_T^i) \rightarrow 0$ then $U_T^i$ converges to a flat annulus with respect to $L^2$ metric convergence. If instead $m_H(\Sigma_T^i)-m_H(\Sigma_0^i) \rightarrow 0$ and $m_H(\Sigma_T^i) \rightarrow m >0$ then we show that $U_T^i$ converges to a topological annulus portion of the Schwarzschild metric with respect to $L^2$ metric convergence.Comment: 31 pages, Lemma 2.10 added, typos corrected. Final version to appear in Annales Henri Poincar

Measuring Inflation Expectations in the Euro Area

This article provides an overview of the main measures of expectations for the euro area and outlines the caveats that must be taken into account when analysing each one.

Recovering a Lost Story Using Oral History: The United States Supreme Court\u27s Historic Green v. New Kent County, Virginia, Decision

In 1965, New Kent County, located just east of Richmond, Virginia, became the setting for the one of the most important school desegregation cases since Brown v. Board of Education. Ten years after the U.S. Supreme Court declared separate but equal unconstitutional, both public schools in New Kent, the George W. Watkins School for blacks and the New Kent School for whites, remained segregated. In 1965, however, local blacks and the Virginia State NAACP initiated a legal challenge to segregated schools, hoping to initiate desegregation where the process had yet to begin and to accelerate the process in areas where token desegregation was the norm. In 1968, the U.S. Supreme Court decision inCharles C. Green v. the School Board of New Kent County forced New Kent County and localities across the state and nation to fulfill the promise of Brown. While the case has been part of the court records since it was decided in 1968, it has remained largely unknown to the general public and many scholars of the era. This article is an attempt to use the tool of oral history to present the people and the story behind Green v. New Kent County and to add another piece to the puzzle that was school desegregation in this country