2011/08/17 by Emil Saucan, Saucan, Emil
Computer Science · Mathematics · #57Q15 #68U05 #83C27 #Differential Geometry (math.DG) #FOS: Computer and information sciences #FOS: Mathematics #Graphics (cs.GR) #Primary: 53C23 #Secondary: 30C65 #cs.GR #math.DG #msc:30C65 #msc:53C23 #msc:57Q15 #msc:68U05 #msc:83C27
paper · pdf · doi:10.48550/arxiv.1108.3529
29 pages
arxiv created 2011/08/17 · arxiv updated 2011/08/18
We study the differential geometric consequences of our previous result on the existence of fat triangulations, in conjunction with a result of Cheeger, Müller and Schrader, regarding the convergence of Lipschitz-Killing curvatures of piecewise-flat approximations of smooth Riemannian manifolds. A further application to the existence of quasiconformal mappings between manifolds, as well as an extension of the triangulation result to the case of almost Riemannian manifolds, are also given. In addition, the notion of fatness of triangulations and its relation to metric curvature and to excess is explored. Moreover, applications of the main results, and in particular a purely metric approach to Regge calculus, are also investigated.