  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. In addition, both maps can be made
arbitrarily close to an isometry. In the appendix, we derive quantitative
estimates of the harmonic radius, so that the estimates on the number of
eigenfunctions or heat kernels needed can be made quantitative as well.
