Abstract
For any n-dimensional compact Riemannian manifold M with smooth metric g, we construct a canonical t-family of isometric embeddings It : M → ℝq(t), with t > 0 sufficiently small and q (t ) 蠑 t-n/2. This is done by intrinsically perturbing the heat kernel embedding introduced in [BBG]. As t → 0+, asymptotic geometry of the embedded images is discussed.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 497-538 |
| Number of pages | 42 |
| Journal | Journal of Differential Geometry |
| Volume | 99 |
| Issue number | 3 |
| DOIs | |
| State | Published - Mar 1 2015 |
All Science Journal Classification (ASJC) codes
- Analysis
- Algebra and Number Theory
- Geometry and Topology