Volume-constrained minimizers for the prescribed curvature problem in periodic media

We establish existence of compact minimizers of the prescribed mean curvature problem with volume constraint in periodic media. As a consequence, we construct compact approximate solutions to the prescribed mean curvature equation. We also show convergence after rescaling of the volume-constrained minimizers towards a suitable Wulff Shape, when the volume tends to infinity.Comment: In this version the statement of Lemma 2.5 has been corrected with respect to the published versio

Retrieving Temperatures and Abundances of Exoplanet Atmospheres with High-Resolution Cross-Correlation Spectroscopy

Hi-resolution spectroscopy (R > 25,000) has recently emerged as one of the leading methods to detect atomic and molecular species in the atmospheres of exoplanets. However, it has so far been lacking in a robust method to extract quantitative constraints on temperature structure and molecular/atomic abundances. In this work we present a novel Bayesian atmospheric retrieval framework applicable to high resolution cross-correlation spectroscopy (HRCCS) that relies upon the cross-correlation between data and models to extract the planetary spectral signal. We successfully test the framework on simulated data and show that it can correctly determine Bayesian credibility intervals on atmospheric temperatures and abundances allowing for a quantitative exploration of the inherent degeneracies. Furthermore, our new framework permits us to trivially combine and explore the synergies between HRCCS and low-resolution spectroscopy (LRS) to provide maximal leverage on the information contained within each. This framework also allows us to quantitatively assess the impact of molecular line opacities at high resolution. We apply the framework to VLT CRIRES K-band spectra of HD 209458 b and HD 189733 b and retrieve abundant carbon monoxide but sub-solar abundances for water, largely invariant under different model assumptions. This confirms previous analysis of these datasets, but is possibly at odds with detections of water at different wavelengths and spectral resolutions. The framework presented here is the first step towards a true synergy between space observatories and ground-based hi-resolution observations.Comment: Accepted Version (01/16/19

Quantitative estimates for bending energies and applications to non-local variational problems

We discuss a variational model, given by a weighted sum of perimeter, bending and Riesz interaction energies, that could be considered as a toy model for charged elastic drops. The different contributions have competing preferences for strongly localized and maximally dispersed structures. We investigate the energy landscape in dependence of the size of the 'charge', i.e. the weight of the Riesz interaction energy. In the two-dimensional case we first prove that for simply connected sets of small elastic energy, the elastic deficit controls the isoperimetric deficit. Building on this result, we show that for small charge the only minimizers of the full variational model are either balls or centered annuli. We complement these statements by a non-existence result for large charge. In three dimensions, we prove area and diameter bounds for configurations with small Willmore energy and show that balls are the unique minimizers of our variational model for sufficiently small charge

Representation, relaxation and convexity for variational problems in Wiener spaces

We show convexity of solutions to a class of convex variational problems in the Gauss and in the Wiener space. An important tool in the proof is a representation formula for integral functionals in this infinite dimensional setting, that extends analogous results valid in the classical Euclidean framework

Conformal Defect Solutions in N=2,D=4N=2,D=4 Gauged Supergravity

We consider conformal defect solutions in four dimensional $N=2$ gauged supergravity. These solutions are constructed as a warped product of $AdS_2\times S^1$ over an interval with non-trivial electric and magnetic fields. We show for minimal gauged supergravity and for gauged supergravity with vector multiplets and abelian gauging that supersymmetric defect solutions are only possible when the geometry has a conical defect in either the bulk or the boundary metric.Comment: 20 pages, no figure

Modelling Dynamic Conditional Correlations in WTI Oil Forward and Futures Returns

This paper estimates the dynamic conditional correlations in the returns on WTI oil one-month forward prices, and one-, three-, six-, and twelve-month futures prices, using recently developed multivariate conditional volatility models. The dynamic correlations enable a determination of whether the forward and various futures returns are substitutes or complements, which are crucial for deciding whether or not to hedge against unforeseen circumstances. The models are estimated using daily data on WTI oil forward and futures prices, and their associated returns, from 3 January 1985 to 16 January 2004. At the univariate level, the estimates are statistically significant, with the occasional asymmetric effect in which negative shocks have a greater impact on volatility than positive shocks. In all cases, both the short- and long-run persistence of shocks are statistically significant. Among the five returns, there are ten conditional correlations, with the highest estimate of constant conditional correlation being 0.975 between the volatilities of the three-month and six-month futures returns, and the lowest being 0.656 between the volatilities of the forward and twelve-month futures returns. The dynamic conditional correlations can vary dramatically, being negative in four of ten cases and being close to zero in another five cases. Only in the case of the dynamic volatilities of the three-month and six-month futures returns is the range of variation relatively narrow, namely (0.832, 0.996). Thus, in general, the dynamic volatilities in the returns in the WTI oil forward and future prices can be either independent or interdependent over time.Constant conditional correlations, Dynamic conditional correlations, Multivariate GARCH models, Forward prices and returns, Futures prices and returns, WTI oil prices

Higher Spin Lifshitz Theories and the KdV-Hierarchy

In this paper three dimensional higher spin theories in the Chern-Simons formulation with gauge algebra $sl(N,R)$ are investigated which have Lifshitz symmetry with scaling exponent $z$. We show that an explicit map exists for all $z$ and $N$ relating the Lifshitz Chern-Simons theory to the $(n,m)$ element of the KdV hierarchy. Furthermore we show that the map and hence the conserved charges are independent of $z$. We derive these result from the Drinfeld-Sokolov formalism of integrable systems.Comment: 40 pages, no figure

Firm Location and Corporate Debt

This study examines the influence of a firm’s geographical location on corporate debt and provides evidence that the higher cost of collecting information on firms distant from urban areas has significant implications on a wide array of corporate debt characteristics. We find that rural firms face higher debt yield spreads and attract smaller and less prestigious bank syndicates than urban firms. Rural firms attempt to reduce their informational disadvantage by relying more on relationship banking. Our results on the effect of location on corporate debt are robust to the inclusion of an extensive set of firm and issue characteristics