Embeddings of Riemannian manifolds with heat kernels and eigenfunctions

Understand

We show that any closed n-dimensional Riemannian manifold can be embedded by a map constructed from heat kernels at a certain time from a finite number of points.

• Both this time and this number can be bounded in terms of the dimension, a lower bound on the Ricci curvature, the injectivity radius and the volume.
• It follows that the manifold can be embedded by a finite number of eigenfunctions of the Laplace operator.
• Again, this number only depends on the geometric bounds and the dimension.