arXiv subjects

Ivan Miranda

Publications and source records attributed to Ivan Miranda.

3 recordsLinked to original sources

arXiv2026

Ambient geometry via min-max widths of embedded circles

We prove a lower bound for the Birkhoff min-max invariant of a Riemannian sphere in terms of the min-max width of its embedded circles. The main tool is a method to induce a sweepout by pairs of points in an embedded circle from a given sweepout of the sphere by closed curves, so that the points of each pair of the induced sweepout lie close to two curves of the ambient sweepout that are close to each other. Moreover, considering a non-compact complete Riemannian manifold, we relate upper bounds for the min-max width of its embedded circles to the existence of continuous functions from the manifold to finite graphs with level sets that have uniformly bounded diameters, thus giving an estimate for its 1-width in Urysohn's quantitative dimension theory. In the specific case of the Euclidean plane, we bound from below the classical width of a simple closed curve by its min-max width. Finally, we prove related rigidity results characterizing the round spheres among Zoll spheres.

math.DG↗

arXiv2026

Finite index constant mean curvature hypersurfaces in low dimensions

We prove that every complete finite index immersed CMC hypersurface is either minimal or compact, provided that the ambient six-dimensional manifold is a Riemannian product of a closed manifold with non-negative sectional curvature and a Euclidean factor. This answers affirmatively a question posed by do Carmo, for this class of ambient spaces, and extends known lower dimensional results. As a consequence, we complete the classification of two-sided, complete weakly stable CMC hypersurfaces immersed in the space forms of positive curvature in dimension six. More generally, we study the class of Riemannian manifolds with bounded curvature and obtain several partial results. In particular, we show that a complete, finite index CMC hypersurface immersed in the hyperbolic six-space with mean curvature vector of length greater than seven is necessarily compact.

math.DG↗

arXiv2023

Evaluacion de la contaminacion del aire por material particulado pm2.5 en la ciudad del cusco respecto de los indices de calidad del aire entre 2017 y 2018

In this scientific article, the data on air pollution by PM2.5 particulate matter was evaluated in different locations in the city of Cusco with respect to the Environmental Quality Indexes (INCA) of the Ministry of the Environment of the Peruvian Government. The results show that air pollution in the city of Cusco is an environmental risk problem. More than 84% of the monitored sites have a bad rating (101-500), the corresponding color is orange. This result shows that the air that citizens of Cusco breathe is of poor quality and the population could experience health problems. The recommendation is to avoid outdoor exercises and activities. In the district of San Jeronimo Cusco, the average concentration has been 125 ug/m3, which corresponds to the INCA interval of more than 125, within the red color threshold for care. The health effects are described as chronic lung and cardiovascular diseases, and the health authority should declare levels of alert. It has been concluded that according to INCA, the air in the city of Cusco is of poor quality and falls within the threshold of the Care State Value (VUEC).

physics.soc-ph↗