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Antonio Bueno

Publications and source records attributed to Antonio Bueno.

33 records · Page 2Linked to original sources
arXiv2019

A Delaunay-type classification result for prescribed mean curvature surfaces in $\mathbb{M}^2(κ)\times\mathbb{R}$

The purpose of this paper is to study immersed surfaces in the product spaces $\mathbb{M}^2(κ)\times\mathbb{R}$, whose mean curvature is given as a $C^1$ function depending on their angle function. This class of surfaces extends widely, among others, the well-known theory of surfaces with constant mean curvature. In this paper we give necessary and sufficient conditions for the existence of prescribed mean curvature spheres, and we describe complete surfaces of revolution proving that they behave as the Delaunay surfaces of CMC type.

math.DG↗
arXiv2019

The Björling problem for prescribed mean curvature surfaces in $\mathbb{R}^3$

In this paper we solve the Björling problem for the class of immersed surfaces in $\mathbb{R}^3$ whose mean curvature is given as an analytic function depending on its Gauss map. As an application, we prove the existence of surfaces with the topology of a Möbius strip for an arbitrary large class of prescribed functions. In particular, we use the Björling problem to construct the first known examples of self-translating solitons of the mean curvature flow with the topology of a Möbius strip in $\mathbb{R}^3$

math.DG↗
arXiv2019

The global geometry of surfaces with prescribed mean curvature in $\mathbb{R}^3$

We develop a global theory for complete hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. This theory extends the usual one of constant mean curvature hypersurfaces in $\mathbb{R}^{n+1}$, and also that of self-translating solitons of the mean curvature flow. For the particular case $n=2$, we will obtain results regarding a priori height and curvature estimates, non-existence of complete stable surfaces, and classification of properly embedded surfaces with at most one end.

math.DG↗
arXiv2019

Rotational hypersurfaces of prescribed mean curvature

We use a phase space analysis to give some classification results for rotational hypersurfaces in $\mathbb{R}^{n+1}$ whose mean curvature is given as a prescribed function of its Gauss map. For the case where the prescribed function is an even function in $\mathbb{S}^n$, we show that a Delaunay-type classification holds for this class of hypersurfaces. We also exhibit examples showing that the behavior of rotational hypersurfaces of prescribed (non-constant) mean curvature is much richer than in the constant mean curvature case.

math.DG↗
arXiv2019

Half-space theorems for properly immersed surfaces in $\mathbb{R}^3$ with prescribed mean curvature

Motivated by the large ammount of results obtained for minimal and positive constant mean curvature surfaces in several ambient spaces, the aim of this paper is to obtain half-space theorems for properly immersed surfaces in $\mathbb{R}^3$ whose mean curvature is given as a prescribed function of its Gauss map. In order to achieve this purpose, we will study the behavior at infinity of a 1-parameter family of properly embedded annuli that are analogous to the usual minimal catenoids.

math.DG↗
arXiv2018

Translating solitons of the mean curvature flow in the space $\mathbb{H}^2\times\mathbb{R}$

In this paper we study the theory of self translating solitons of the mean curvature flow of immersed surfaces in the product space $\mathbb{H}^2\times\mathbb{R}$. We relate this theory to the one of manifolds with density, and exploit this relation by regarding these translating solitons as minimal surfaces in a conformal metric space. Explicit examples of these surfaces are constructed, and we study the asymptotic behaviour of the existing rotationally symmetric examples. Finally, we prove some uniqueness and non-existence theorems.

math.DG↗
arXiv2018

Prescribed mean curvature surfaces in the product spaces $\mathbb{M}^2(κ)\times\mathbb{R}$; Height estimates and classification results for properly embedded surfaces

The aim of this paper is to extend classic results of the theory of CMC surfaces in the product spaces to the class of immersed surfaces in $\mathbb{M}^2(κ)\times\mathbb{R}$ whose mean curvature is given as a $C^1$ function depending on their angle function. We cover topics such as the existence of a priori curvature estimates for graphs, height estimates for horizontal and vertical compact graphs and a structure-type result, which classifies all the simply connected, properly embedded surfaces with finite topology.

math.DG↗
arXiv2016

Measurement of the Radiation Energy in the Radio Signal of Extensive Air Showers as a Universal Estimator of Cosmic-Ray Energy

We measure the energy emitted by extensive air showers in the form of radio emission in the frequency range from 30 to 80 MHz. Exploiting the accurate energy scale of the Pierre Auger Observatory, we obtain a radiation energy of 15.8 \pm 0.7 (stat) \pm 6.7 (sys) MeV for cosmic rays with an energy of 1 EeV arriving perpendicularly to a geomagnetic field of 0.24 G, scaling quadratically with the cosmic-ray energy. A comparison with predictions from state-of-the-art first-principle calculations shows agreement with our measurement. The radiation energy provides direct access to the calorimetric energy in the electromagnetic cascade of extensive air showers. Comparison with our result thus allows the direct calibration of any cosmic-ray radio detector against the well-established energy scale of the Pierre Auger Observatory.

astro-ph.HE↗
arXiv2016

Energy Estimation of Cosmic Rays with the Engineering Radio Array of the Pierre Auger Observatory

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30 to 80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy -- corrected for geometrical effects -- is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.

astro-ph.HE↗
arXiv2015

Measurement of the cosmic ray spectrum above $4{\times}10^{18}$ eV using inclined events detected with the Pierre Auger Observatory

A measurement of the cosmic-ray spectrum for energies exceeding $4{\times}10^{18}$ eV is presented, which is based on the analysis of showers with zenith angles greater than $60^{\circ}$ detected with the Pierre Auger Observatory between 1 January 2004 and 31 December 2013. The measured spectrum confirms a flux suppression at the highest energies. Above $5.3{\times}10^{18}$ eV, the "ankle", the flux can be described by a power law $E^{-γ}$ with index $γ=2.70 \pm 0.02 \,\text{(stat)} \pm 0.1\,\text{(sys)}$ followed by a smooth suppression region. For the energy ($E_\text{s}$) at which the spectral flux has fallen to one-half of its extrapolated value in the absence of suppression, we find $E_\text{s}=(5.12\pm0.25\,\text{(stat)}^{+1.0}_{-1.2}\,\text{(sys)}){\times}10^{19}$ eV.

astro-ph.HE↗
arXiv2015

An improved limit to the diffuse flux of ultra-high energy neutrinos from the Pierre Auger Observatory

Neutrinos in the cosmic ray flux with energies near 1 EeV and above are detectable with the Surface Detector array of the Pierre Auger Observatory. We report here on searches through Auger data from 1 January 2004 until 20 June 2013. No neutrino candidates were found, yielding a limit to the diffuse flux of ultra-high energy neutrinos that challenges the Waxman-Bahcall bound predictions. Neutrino identification is attempted using the broad time-structure of the signals expected in the SD stations, and is efficiently done for neutrinos of all flavors interacting in the atmosphere at large zenith angles, as well as for "Earth-skimming" neutrino interactions in the case of tau neutrinos. In this paper the searches for downward-going neutrinos in the zenith angle bins $60^\circ-75^\circ$ and $75^\circ-90^\circ$ as well as for upward-going neutrinos, are combined to give a single limit. The $90\%$ C.L. single-flavor limit to the diffuse flux of ultra-high energy neutrinos with an $E^{-2}$ spectrum in the energy range $1.0 \times 10^{17}$ eV - $2.5 \times 10^{19}$ eV is $E_ν^2 dN_ν/dE_ν< 6.4 \times 10^{-9}~ {\rm GeV~ cm^{-2}~ s^{-1}~ sr^{-1}}$.

astro-ph.HE↗
arXiv2015

Status of the Silicon Photomultiplier Telescope FAMOUS for the Fluorescence Detection of UHECRs

An established technique for the measurement of ultra-high-energy-cosmic-rays is the detection of the fluorescence light induced in the atmosphere of the Earth, by means of telescopes equipped with photomultiplier tubes. Silicon photomultipliers (SiPMs) promise an increase in the photon detection efficiency which outperforms conventional photomultiplier tubes. In combination with their compact package, a moderate bias voltage of several ten volt and single photon resolution, the use of SiPMs can improve the energy and spatial resolution of air fluorescence measurements, and lead to a gain in information on the primary particle. Though, drawbacks like a high dark-noise-rate and a strong temperature dependency have to be managed. FAMOUS is a refracting telescope prototype instrumented with 64 SiPMs of which the main optical element is a Fresnel lens of 549.7 mm diameter and 502.1 mm focal length. The sensitive area of the SiPMs is increased by a special light collection system consisting of Winston cones. The total field of view of the telescope is approximately 12 $^\circ$. The frontend electronics automatically compensates for the temperature dependency of the SiPMs and will provide trigger information for the readout. Already for this prototype, the Geant4 detector simulation indicates full detection efficiency of extensive air showers of $E=10^{18}\,\text{eV}$ up to a distance of 6 km. We present the first working version of FAMOUS with a focal plane prototype providing seven active pixels.

astro-ph.IM↗
arXiv2014

Translation surfaces of linear Weingarten type

We give a relatively simple proof that a translation surface in Euclidean space that satisfies a relation of type $aH+bK=c$, for some real numbers $a,b,c$, where $H$ and $K$ are the mean curvature and the Gauss curvature of the surface, respectively, must have $a=0$ or $b=0$, and thus, $K$ is constant or $H$ is constant. Our method of proof extends to the Lorentzian ambient space.

math.DG↗