Geometry and Topology Seminar 2019-2020
|September 29||Ke Zhu(Minnesota State University)||Isometric Embedding via Heat Kernel||Bing Wang|
|October 6||Shaosai Huang(Stony Brook)||TBA||Bing Wang|
|October 20||Shengwen Wang (Johns Hopkins)||TBA||Lu Wang|
|October 27||Marco Mendez-Guaraco (Chicago)||TBA||Lu Wang|
|November 17||Ovidiu Munteanu (University of Connecticut)||TBA||Bing Wang|
"Isometric Embedding via Heat Kernel"
The Nash embedding theorem states that every Riemannian manifold can be isometrically embedded into some Euclidean space with dimension bound. Isometric means preserving the length of every path. Nash's proof involves sophisticated perturbations of the initial embedding, so not much is known about the geometry of the resulted embedding.
In this talk, using the eigenfunctions of the Laplacian operator, we construct canonical isometric embeddings of compact Riemannian manifolds into Euclidean spaces, and study the geometry of embedded images. They turn out to have large mean curvature (intuitively, very bumpy), but the extent of oscillation is about the same at every point. This is a joint work with Xiaowei Wang.
Archive of past Geometry seminars