Searcharxiv⌕ Search

arXiv subjects

Carlos Duran

Publications and source records attributed to Carlos Duran.

5 recordsLinked to original sources
arXiv2021

The Atacama Large Aperture Submillimetre Telescope (AtLAST)

The coldest and densest structures of gas and dust in the Universe have unique spectral signatures across the (sub-)millimetre bands ($ν\approx 30-950$~GHz). The current generation of single dish facilities has given a glimpse of the potential for discovery, while sub-mm interferometers have presented a high resolution view into the finer details of known targets or in small-area deep fields. However, significant advances in our understanding of such cold and dense structures are now hampered by the limited sensitivity and angular resolution of our sub-mm view of the Universe at larger scales. In this context, we present the case for a new transformational astronomical facility in the 2030s, the Atacama Large Aperture Submillimetre Telescope (AtLAST). AtLAST is a concept for a 50-m-class single dish telescope, with a high throughput provided by a 2~deg - diameter Field of View, located on a high, dry site in the Atacama with good atmospheric transmission up to $ν\sim 1$~THz, and fully powered by renewable energy. We envision AtLAST as a facility operated by an international partnership with a suite of instruments to deliver the transformative science that cannot be achieved with current or in-construction observatories. As an 50m-diameter telescope with a full complement of advanced instrumentation, including highly multiplexed high-resolution spectrometers, continuum cameras and integral field units, AtLAST will have mapping speeds hundreds of times greater than current or planned large aperture ($>$ 12m) facilities. By reaching confusion limits below L$_*$ in the distant Universe, resolving low-mass protostellar cores at the distance of the Galactic Centre, and directly mapping both the cold and the hot (the Sunyaev-Zeldovich effect) circumgalactic medium of galaxies, AtLAST will enable a fundamentally new understanding of the sub-mm Universe.

astro-ph.IM↗
arXiv2015

Sharp constant in Riemannian L^p-Gagliardo-Nirenberg inequalities

Let (M,g) be a smooth compact Riemannian manifold of dimension n \geq 2, 1 < p < n and 1 \leq q < r < p^\ast = \frac{np}{n-p} be real parameters. This paper concerns to the validity of the optimal Gagliardo-Nirenberg inequality (\int_M |u|^r\; dv_g)^{\fracτ{r θ}} \leq (A_{opt} (\int_M |\nabla_g u|^p\; dv_g)^{\fracτ{p}} + B_{opt} (\int_M |u|^p\; dv_g)^{\fracτ{p}}) (int_M |u|^q\; dv_g)^{\frac{τ(1 - θ)}{θq}} \; . This kind of inequality is studied in Chen and Sun (Nonlinear Analysis 72 (2010), pp. 3159-3172) where the authors established its validity when 2 < p < r < p^\ast and (implicitly) τ= 2. Here we solve the case p \geq r and introduce one more parameter 1 \leq τ\leq \min\{p,2\}. Moreover, we prove the existence of extremal function for the optimal inequality above.

math.AP↗
arXiv2006

A minimal Brieskorn 5-sphere in the Gromoll-Meyer sphere and its applications

We recognize the Gromoll-Meyer sphere Sigma^7 as the geodesic join of a simple closed geodesic and a minimal subsphere Sigma^5, which can be equivariantly identified with the Brieskorn sphere W^5_3. As applications we in particular determine the full isometry group of Sigma^7, classify all closed subgroups that act freely, determine the homotopy type of the corresponding orbit spaces, identify the Hirsch-Milnor involution in dimension 5 with the Calabi involution of W^5_3, and obtain explicit formulas for diffeomorphisms between the Brieskorn spheres W^5_3 and W^13_3 with standard Euclidean spheres.

math.DG↗
arXiv2005

Wiedersehen metrics and exotic involutions of Euclidean spheres

We provide explicit, simple, geometric formulas for free involutions rho of Euclidean spheres that are not conjugate to the antipodal involution. Therefore the quotient S^n/rho is a manifold that is homotopically equivalent but not diffeomorphic to RP^n. We use these formulas for constructing explicit non-trivial elements in pi_1 Diff(S^5) and pi_1 Diff(S^13) and to provide explicit formulas for non-cancellation phenomena in group actions.

math.GT↗