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We use mass-transportation as a tool to compare surfaces (2-manifolds). In particular, we determine the similarity of two given surfaces by solving a mass-transportation problem between their conformal densities. This mass transportation problem differs from the standard case in that we require the solution to be invariant under global Mobius transformations. Our approach provides a constructive way of defining a metric in the abstract space of simply-connected smooth surfaces with boundary (i.e. surfaces of disk-type); this metric can also be used to define meaningful intrinsic distances between pairs of patches in the two surfaces, which allows automatic alignment of the surfaces. We provide numerical experiments on real-life surfaces to demonstrate possible applications in natural sciences.
We prove that every finitely generated Kleinian group that contains a finite, non-cyclic subgroup either is finite or virtually free or contains a surface subgroup. Hence, every arithmetic Kleinian group contains a surface subgroup.
We investigate the isogeometric analysis for surface PDEs based on the extended Loop subdivision approach. The basis functions consisting of quartic box-splines corresponding to each subdivided control mesh are utilized to represent the geometry exac
Three dimensional surface reconstruction based on two dimensional sparse information in the form of only a small number of level lines of the surface with moderately complex structures, containing both structured and unstructured geometries, is consi
The paper analyzes and compares some spectral filtering methods as truncated singular/eigen-value decompositions and Tikhonov/Re-blurring regularizations in the case of the recently proposed Reflective [M.K. Ng, R.H. Chan, and W.C. Tang, A fast algor
The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian case corresp