On the Invariant Theory of Weingarten Surfaces in Euclidean Space

We prove that any strongly regular Weingarten surface in Euclidean space carries locally geometric principal parameters. The basic theorem states that any strongly regular Weingarten surface is determined up to a motion by its structural functions and the normal curvature function satisfying a geometric differential equation. We apply these results to the special Weingarten surfaces: minimal surfaces, surfaces of constant mean curvature and surfaces of constant Gauss curvature.Comment: 16 page

The subelliptic heat kernel on SU(2): Representations, Asymptotics and Gradient bounds

The Lie group SU(2) endowed with its canonical subriemannian structure appears as a three-dimensional model of a positively curved subelliptic space. The goal of this work is to study the subelliptic heat kernel on it and some related functional inequalities.Comment: Update: Added section + Correction of typo

Sedimentation rates in the central lake constance determined with210Pb and137Cs

Sediment cores from central Lake Constance were dated with210Pb and137Cs. A sedimentation rate of (0.11±0.02) g·cm-2·y-1 was determined with the210Pb method.137Cs measurements revealed sedimentation rates of (0.11±0.01) g·cm-2·y-1 and (0.08±0.01) g·cm-2·y-1 respectively for two different cores sampled at the same location. The lower Cs-dated value indicates incomplete core recovery and demonstrates the sensitivity of this simple dating method to small losses of material at the water/sediment interface. An unambiguous application of the137Cs method is, therefore, only possible if complete core recovery is ensured. Sedimentation rates based on particulate matter, collected in sediment traps at various water depths, agree with the results of the radioisotope methods. Estimates of 30-125 days residence times for suspended particulate matter were calculated from7Be measurements. © 1987 Birkhäuser Verlag

Generalized Ricci Curvature Bounds for Three Dimensional Contact Subriemannian manifolds

Measure contraction property is one of the possible generalizations of Ricci curvature bound to more general metric measure spaces. In this paper, we discover sufficient conditions for a three dimensional contact subriemannian manifold to satisfy this property.Comment: 49 page

First direct detection of an exoplanet by optical interferometry; Astrometry and K-band spectroscopy of HR8799 e

To date, infrared interferometry at best achieved contrast ratios of a few times $10^{-4}$ on bright targets. GRAVITY, with its dual-field mode, is now capable of high contrast observations, enabling the direct observation of exoplanets. We demonstrate the technique on HR8799, a young planetary system composed of four known giant exoplanets. We used the GRAVITY fringe tracker to lock the fringes on the central star, and integrated off-axis on the HR8799e planet situated at 390 mas from the star. Data reduction included post-processing to remove the flux leaking from the central star and to extract the coherent flux of the planet. The inferred K band spectrum of the planet has a spectral resolution of 500. We also derive the astrometric position of the planet relative to the star with a precision on the order of 100$\,\mu$as. The GRAVITY astrometric measurement disfavors perfectly coplanar stable orbital solutions. A small adjustment of a few degrees to the orbital inclination of HR 8799 e can resolve the tension, implying that the orbits are close to, but not strictly coplanar. The spectrum, with a signal-to-noise ratio of $\approx 5$ per spectral channel, is compatible with a late-type L brown dwarf. Using Exo-REM synthetic spectra, we derive a temperature of $1150\pm50$\,K and a surface gravity of $10^{4.3\pm0.3}\,$cm/s$^{2}$. This corresponds to a radius of $1.17^{+0.13}_{-0.11}\,R_{\rm Jup}$ and a mass of $10^{+7}_{-4}\,M_{\rm Jup}$, which is an independent confirmation of mass estimates from evolutionary models. Our results demonstrate the power of interferometry for the direct detection and spectroscopic study of exoplanets at close angular separations from their stars.Comment: published in A&

Flux Modulations seen by the Muon Veto of the GERDA Experiment

The GERDA experiment at LNGS of INFN is equipped with an active muon veto. The main part of the system is a water Cherenkov veto with 66~PMTs in the water tank surrounding the GERDA cryostat. The muon flux recorded by this veto shows a seasonal modulation. Two effects have been identified which are caused by secondary muons from the CNGS neutrino beam (2.2 %) and a temperature modulation of the atmosphere (1.4 %). A mean cosmic muon rate of $I^0_{\mu} = (3.477 \pm 0.002_{\textrm{stat}} \pm 0.067_{\textrm{sys}}) \times 10^{-4}$/(s$\cdot$m$^2$) was found in good agreement with other experiments at LNGS at a depth of 3500~meter water equivalent.Comment: 7 pages, 6 figure

Ricci curvature of finite Markov chains via convexity of the entropy

We study a new notion of Ricci curvature that applies to Markov chains on discrete spaces. This notion relies on geodesic convexity of the entropy and is analogous to the one introduced by Lott, Sturm, and Villani for geodesic measure spaces. In order to apply to the discrete setting, the role of the Wasserstein metric is taken over by a different metric, having the property that continuous time Markov chains are gradient flows of the entropy. Using this notion of Ricci curvature we prove discrete analogues of fundamental results by Bakry--Emery and Otto--Villani. Furthermore we show that Ricci curvature bounds are preserved under tensorisation. As a special case we obtain the sharp Ricci curvature lower bound for the discrete hypercube.Comment: 39 pages, to appear in Arch. Ration. Mech. Ana

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page

The first search for bosonic super-WIMPs with masses up to 1 MeV/c2^2 with GERDA

We present the first search for bosonic super-WIMPs as keV-scale dark matter candidates performed with the GERDA experiment. GERDA is a neutrinoless double-beta decay experiment which operates high-purity germanium detectors enriched in $^{76}$Ge in an ultra-low background environment at the Laboratori Nazionali del Gran Sasso (LNGS) of INFN in Italy. Searches were performed for pseudoscalar and vector particles in the mass region from 60 keV/c$^2$ to 1 MeV/c$^2$. No evidence for a dark matter signal was observed, and the most stringent constraints on the couplings of super-WIMPs with masses above 120 keV/c$^2$ have been set. As an example, at a mass of 150 keV/c$^2$ the most stringent direct limits on the dimensionless couplings of axion-like particles and dark photons to electrons of $g_{ae} < 3 \cdot 10^{-12}$ and ${\alpha'}/{\alpha} < 6.5 \cdot 10^{-24}$ at 90% credible interval, respectively, were obtained.Comment: 6 pages, 3 figures, submitted to Physical Review Letters, added list of authors, updated ref. [21