The Analytic Torsion of the cone over an odd dimensional manifold

We study the analytic torsion of the cone over an orientable odd dimensional compact connected Riemannian manifold W. We prove that the logarithm of the analytic torsion of the cone decomposes as the sum of the logarithm of the root of the analytic torsion of the boundary of the cone, plus a topological term, plus a further term that is a rational linear combination of local Riemannian invariants of the boundary. We also prove that this last term coincides with the anomaly boundary term appearing in the Cheeger Muller theorem for a manifold with boundary, according to Bruning and Ma, either in the case that W is an odd sphere or has dimension smaller than six. It follows in particular that the Cheeger Muller theorem holds for the cone over an odd dimensional sphere. We also prove Poincare duality for the analytic torsion of a cone

The analytic torsion of the finite metric cone over a compact manifold

We give an explicit formula for the $L^2$ analytic torsion of the finite metric cone over an oriented compact connected Riemannian manifold. We provide an interpretation of the different factors appearing in this formula. We prove that the analytic torsion of the cone is the finite part of the limit obtained collapsing one of the boundaries, of the ratio of the analytic torsion of the frustum to a regularising factor. We show that the regularising factor comes from the set of the non square integrable eigenfunctions of the Laplace Beltrami operator on the cone.Comment: To appear in Journal of the Mathematical Society of Japa

The analytic torsion of a cone over a sphere

We compute the analytic torsion of a cone over a sphere of dimension 1, 2, and 3, and we conjecture a general formula for the cone over an odd dimensional sphere

THE IPAD PRO BUILT-IN LIDAR SENSOR: 3D RAPID MAPPING TESTS AND QUALITY ASSESSMENT

The main goal of this ongoing research is the evaluation of the iPad Pro built-in LiDAR sensor for large scale 3D rapid mapping. Different aspects have been considered from the architectural surveying perspective and several analyses were carried out focusing on the acquisition phase and the definition of best practices for data collection, the quantitative analysis on the acquired data and their 3D positional accuracy assessment, and the qualitative analysis of the achievable metric products. Despite this paper is a preliminary analysis and deeper studies in various application environment are necessary, the availability of a LiDAR sensor embedded in a tablet or mobile phone, appears promising for rapid surveying purposes. According to test outcomes, the sensor is able to rapidly acquire reliable 3D point clouds suitable for 1:200 architectural rapid mapping; the iPad Pro could represent an interesting novelty also thanks to its price (compared to standard surveying instruments), portability and limited time required both for data acquisition and processing

THE IPAD PRO BUILT-IN LIDAR SENSOR: 3D RAPID MAPPING TESTS AND QUALITY ASSESSMENT

Abstract. The main goal of this ongoing research is the evaluation of the iPad Pro built-in LiDAR sensor for large scale 3D rapid mapping. Different aspects have been considered from the architectural surveying perspective and several analyses were carried out focusing on the acquisition phase and the definition of best practices for data collection, the quantitative analysis on the acquired data and their 3D positional accuracy assessment, and the qualitative analysis of the achievable metric products. Despite this paper is a preliminary analysis and deeper studies in various application environment are necessary, the availability of a LiDAR sensor embedded in a tablet or mobile phone, appears promising for rapid surveying purposes. According to test outcomes, the sensor is able to rapidly acquire reliable 3D point clouds suitable for 1:200 architectural rapid mapping; the iPad Pro could represent an interesting novelty also thanks to its price (compared to standard surveying instruments), portability and limited time required both for data acquisition and processing