A Spectral Bernstein Theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface $M$ in $\R^{n+1}$. (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that $M$ has only essential spectrum consisting of the half line $[0, +\infty)$. This is the case when $\lim_{\tilde{r}\to +\infty}\tilde{r}\kappa_i=0$, where $\tilde{r}$ is the extrinsic distance to a point of $M$ and $\kappa_i$ are the principal curvatures. (2) If the $\kappa_i$ satisfy the decay conditions $|\kappa_i|\leq 1/\tilde{r}$, and strict inequality is achieved at some point $y\in M$, then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.Comment: 16 pages. v2. Final version: minor revisions, we add Proposition 3.2. Accepted for publication in the Annali di Matematica Pura ed Applicata, on the 05/03/201

Cosmological Experiments in Condensed Matter Systems

Topological defects are thought to be left behind by the cosmological phase transitions which occur as the universe expands and cools. Similar processes can be studied in the phase transitions which take place in the laboratory: ``Cosmological'' experiments in superfluid He$^4$ and in liquid crystals were carried out within the past few years, and their results shed a new light on the dynamics of the defect-formation process. The aim of this paper is to review the key ideas behind this cosmology - condensed matter connection and to propose new experiments which could probe heretofore unaddressed aspects of the topological defects formation process.Comment: 64 pages (TeX), figures not included, in press Phys.Re

The importance of structural model availability on seismic interpretation

The authors thank Graham Yielding and Douglas Paton for their kind and supportive comments on the paper. BP/GUPCO are acknowledged for providing data from the Gulf of Suez. The authors acknowledge the support of MVE and use of Move software 2015.2 for this work. Juan Alcalde is funded by NERC grant NE/M007251/1, on interpretational uncertainty. The work could not have been completed without the support of the students of Integrated Petroleum Geoscience Master of Science degree at the University of Aberdeen (United Kingdom) who took part in the interpretation experiment.Peer reviewedPublisher PD

New concepts in nuclear arms control Verified cutoff and verified disposal

SIGLEAvailable from British Library Document Supply Centre- DSC:6579.1775(PPNN-OP--5) / BLDSC - British Library Document Supply CentreGBUnited Kingdo