Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is \C_+. $F$ is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C^{m,\al}, $m\ge4$.Comment: 9 pages, v2:final version, to be publishe

Remission during pregnancy of severe Chronic Hypertension due to 11-ß Hydroxylase Deficiency

When hypertension is a result of an underlying identifiable abnormality, the latter's early discovery can lead to a timely cure of the hypertension and the prevention of its complications. We present a case of high blood pressure lowered by pregnancy, suggestive of an endocrine cause. This was confirmed following a detailed history which revealed severe hypertension intractable to therapy, yet which remitted during pregnancy. A diagnosis of 11-beta hydroxylase deficiency was made consequent upon the finding of raised serum 11-desoxycorticosterone levels. The blood pressure was finally controlled with glucocorticoid replacement therapy and spironolactone.peer-reviewe

Non-scale-invariant inverse curvature flows in Euclidean space

We consider the inverse curvature flows $\dot x=F^{-p}\nu$ of closed star-shaped hypersurfaces in Euclidean space in case $0<p\not=1$ and prove that the flow exists for all time and converges to infinity, if $0<p<1$, while in case $p>1$, the flow blows up in finite time, and where we assume the initial hypersurface to be strictly convex. In both cases the properly rescaled flows converge to the unit sphere.Comment: 21 pages, this is the published versio

Technology and politics: The regional airport experience

The findings of a comparative study of the following six regional airports were presented: Dallas/Fort Worth, Kansas City, Washington, D.C., Montreal, Tampa, and St. Louis. Each case was approached as a unique historical entity, in order to investigate common elements such as: the use of predictive models in planning, the role of symbolism to heighten dramatic effects, the roles of community and professional elites, and design flexibility. Some of the factors considered were: site selection, consolidation of airline service, accessibility, land availability and cost, safety, nuisance, and pollution constraints, economic growth, expectation of regional growth, the demand forecasting conundrum, and design decisions. The hypotheses developed include the following: the effect of political, social, and economic conflicts, the stress on large capacity and dramatic, high-technology design, projections of rapid growth to explain the need for large capital outlays

The Rhetoric of Judicial Critique: From Judicial Restraint to the Virtual Bill of Rights

Professor Michael Gerhardt traces the rhetoric employed by national leaders and commentators over the past century to describe popular conceptions of the judicial function. In particular, Professor Gerhardt examines the evolution of the terminology used in popular and political rhetoric, revealing their inconsistent application to political ideologies through time. Professor Gerhardt argues that such shifts in usage correspond with transfers of power between the political authorities controlling the central interests at stake in constitutional adjudication. Professor Gerhardt applies the shortcomings of traditional political rhetoric to the issues surrounding technological advancements, concluding that the proper treatment of technology by the Supreme Court in the twenty-first century will require recognition of the complex consequences posed by these advances

Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature

We prove convergence results for expanding curvature flows in the Euclidean and hyperbolic space. The flow speeds have the form $F^{-p}$, where $p>1$ and $F$ is a positive, strictly monotone and 1-homogeneous curvature function. In particular this class includes the mean curvature $F=H$. We prove that a certain initial pinching condition is preserved and the properly rescaled hypersurfaces converge smoothly to the unit sphere. We show that an example due to Andrews-McCoy-Zheng can be used to construct strictly convex initial hypersurfaces, for which the inverse mean curvature flow to the power $p>1$ loses convexity, justifying the necessity to impose a certain pinching condition on the initial hypersurface.Comment: 18 pages. We included an example for the loss of convexity and pinching. In the third version we dropped the concavity assumption on F. Comments are welcom