17 citations · 49 across the 8 of their papers we have counts for
5 papers · 1 filter
From Varadhan's Limit to Eigenmaps: A Guide to the Geometric Analysis behind Manifold Learning
Chen-Yun Lin, Christina Sormani
We present an overview of the history of the heat kernel and eigenfunctions on Riemannian manifolds and how the theory has lead to modern methods of analyzing high dimensional data…
Manifold embeddings by heat kernels of connection Laplacian
Chen-Yun Lin
We show that any closed -dimensional manifold can be embedded by a map constructed using the heat kernels of the connection Laplacian as well as a maps constructed using…
Embeddings of Riemannian Manifolds with Finite Eigenvector Fields of Connection Laplacian
Chen-Yun Lin, Hau-Tieng Wu
We study the problem asking if one can embed manifolds into finite dimensional Euclidean spaces by taking finite number of eigenvector fields of the connection Laplacian. This prob…
Bartnik's mass and Hamilton's Modified Ricci Flow
Chen-Yun Lin, Christina Sormani
We provide estimates on the Bartnik mass of constant mean curvature (CMC) surfaces which are diffeomorphic to spheres and have positive mean curvature. We prove that the Bartnik ma…
Parabolic Constructions of Asymptotically Flat 3-metrics of Prescribed Scalar Curvature
Chen-Yun Lin
In 1993, Bartnik introduced a quasi-spherical construction of metrics of prescribed scalar curvature on 3-manifolds. Under quasi-spherical ansatz, the problem is converted into the…