17 citations · 36 across the 5 of their papers we have counts for
6 papers
The Gauss dual Minkowski problem
Na Fu, Jianping Sun
This article introduces the -Gauss dual curvature measure and proposes its related -Gauss dual Minkowski problem as: for , under what necessary and/or s…
Convergence of Laplacian Spectra from Point Clouds
Zuoqiang Shi, Jian Sun
The spectral structure of the Laplacian-Beltrami operator (LBO) on manifolds has been widely used in many applications, include spectral clustering, dimensionality reduction, mesh…
Point Integral Method for Solving Poisson-type Equations on Manifolds from Point Clouds with Convergence Guarantees
Zhen Li, Zuoqiang Shi, Jian Sun
Partial differential equations (PDE) on manifolds arise in many areas, including mathematics and many applied fields. Among all kinds of PDEs, the Poisson-type equations including…
Convergence of the Point Integral method for Poisson equation on point cloud
Zuoqiang Shi, Jian Sun
The Laplace-Beltrami operator (LBO) is a fundamental object associated to Riemannian manifolds, which encodes all intrinsic geometry of the manifolds and has many desirable propert…
Convergence of the Point Integral method for the Poisson equation with Dirichlet boundary on point cloud
Zuoqiang Shi, Jian Sun
The Poisson equation on manifolds plays an fundamental role in many applications. Recently, we proposed a novel numerical method called the Point Integral method (PIM) to solve the…
Approximating Loops in a Shortest Homology Basis from Point Data
Tamal K. Dey, Jian Sun, Yusu Wang
Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering applications.…