Metric curvatures and their applications. I. (Q344416)

The author gives a survey on metric geometry and suggests a number of applications in imaging and graphics.NEWLINENEWLINEHe discusses what geometry to use and why; he comments on differential geometry and curvature. He introduces a large number of concepts and explores their relations. The aim is to use these concepts in Regge calculus and in graphics.NEWLINENEWLINEHere are some of the concepts that are introduced and discussed by the author: Gromov-Hausdorff distance, Hausdorff distance, Lipschitz distance, Menger curvature, Alt curvature, Haantjes curvature, excess, metric curvature applications, quasi-isometry (or bi-Lipschitz mapping), chord-arc surface, \(\varepsilon\)-flat, DNA microarray analysis, Menger curvature in pattern recognition, Wald curvature, metric quadruple, embedding curvature \(\kappa(Q)\), sectional curvature, Ricci curvature, scalar curvature, Wald-Berestovskii curvature, Riemannian curvature tensor, Lipschitz-Killing curvatures, thick triangulations, spherical simplex, normal cone, dihedral angle, thickness metric curvature and excess, almost Riemannian space.